Chair Professor of Engineering Mathematics
　 Professor Colin Rogers
BA(Oxford), MEd(Toronto), MSc, PhD, DSc(Nottingham)

Office

Email
Telephone
Fax

HJ637, Stanley Ho Building

macolinr@polyu.edu.hk
(852) 2766 4592
(852) 2362 9045

　 　 　 　
　 　

　

　

　

Distinctions

　

　 　
  • Fellow of the Australian Academy of Science
  • Fellow of the Institute of Physics (UK)
  • Centennial Medal (Australian Government Award)
  • Hannan Medal, Australian Academy of Sciences
 　
　

　

　

　

Research Interests

　

 　
　 　
  • Invariance Principles and their Application in Nonlinear Continuum Mechanics
  • Bäcklund Transformations and the Geometry of Soliton Theory
　
　

　

　

　

Adjunct Positions

　

 　
　 　
  • Partner Investigator, Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems
  • Visiting Professorial Fellow, University of New South Wales, Australia
 　
　 　 　 　
　

　

　

　

Principal Publications

　

 　
　
  1. C. Rogers, Reciprocal Relations in Non-Steady One-Dimensional Gasdynamics, Zeit angew. Math. Phys., 19, 58-63 (1968).
  2. C. Rogers, Invariant Transformations in Non-Steady Gasdynamics and Magneto-Gasdynamics, Zeit. angew. Math. Phys., 20, 370-382 (1969).
  3. G. Power, C. Rogers and R.A. Osborn, Bäcklund and Generalised Legendre Transformations in Gasdynamics, Zeit. angew. Math. Mech, 49, 333-340 (1969).
  4. G. Power and C. Rogers, Substitution Principles in Non-Steady Magneto-Gasdynamics, Appl. Sci. Res., 21, 176-184 (1969).
  5. C. Rogers, Transformari Bäcklund in Magnetogazodinamica Liniara Nedisipativa: Rev. Roum. Sci. Techn. Mec. Appl., 15, 371-380 (1970).
  6. C. Rogers and J.G. Kingston, An Analysis of Certain Two Dimensional Non-Steady Gasdynamic Flows, Archives of Mechanics, 22, 411-420 (1970).
  7. J.G. Kingston and C. Rogers, A Class of Polytropic Flows in Plane Non-Steady Magneto-Gasdynamics, Int. J. Engng. Sci., 9, 17-24 (1971).
  8. C. Rogers, J.G. Kingston and S.P. Castell, The Reduction to Canonical Form of Hodograph Equations in Elliptic Diabatic Flow, Acta Phys. Austriaca, 34, 242-250 (1971).
  9. C. Rogers and S.P. Castell, A Parametrisation and Non Uniform Shock Waves in Quasi-One-Dimensional Non-Steady Oblique Field Magneto-Gasdynamics, Acta Mechanica, 13, 255-263 (1972).
  10. C. Rogers, Invariance Properties in Compressible Flow and the Generation of Reciprocal and Adjoint Relations as Bäcklund Transformations, Tensor, 23, 1-10 (1972).
  11. C. Rogers, Bäcklund Transformations and Invariance Properties in Axially Symmetric Flow, Annales de la Societe Scientifique de Bruxelles, 86, 211-219 (1972).
  12. C. Rogers, The Construction of Invariant Transformations in Plane Rotational Gasdynamics, Arch. Rat. Mech. Anal., 47, 36-46 (1972).
  13. C. Rogers and J.G. Kingston, Bäcklund Transformations with Inversion Applied to Stokes Beltrami Equations, Tensor, 24, 322-328 (1972) (invited paper).
  14. C. Rogers, Non-Dissipative Conducting Flows with Hj Lines in the Osculating Plane of the Streamlines, Can. J. Phys., 51, 1335-1340 (1973).
  15. C. Rogers and J.G. Kingston, Application of Bäcklund Transformations to the Stokes Beltrami Equations, J. Austr. Math. Soc., 15, 179-189 (1973).
  16. D.L. Clements and C. Rogers, On Wave Propagation in Inhomogeneous Elastic Media, Int. J. Solids and Structures, 10, 661-669 (1974).
  17. C. Rogers and J.G. Kingston, Non-Dissipative Magnetohydrodynamic Flows with Magnetic and Velocity Field Lines Orthogonal Geodesics on a Normal Congruence, Soc. Ind. Appl. Math. J. on Applied Mathematics, 26, 183-195 (1974).
  18. D.L. Clements and C. Rogers, On the Application of a Bäcklund Transformation to Linear Isotropic Elasticity, J. Inst. Math. Appl., 14, 23-30 (1974).
  19. D.L. Clements and C. Rogers, Wave Propagation in (N+1)-dimensional Spherically Symmetric Inhomogeneous Elastic Media, Can. J. Phys., 52, 1246-1252 (1974).
  20. S.P. Castell and C. Rogers, Application of Invariant Transformations in One-Dimensional Non-Steady Gasdynamics, Quart. Appl. Math., 32, 241-251 (1974).
  21. S.P. Castell and C. Rogers, A Note on the Physical Requirements for the Existence of Certain Non-Uniform Shock Waves in Magneto-Gasdynamics, Acta Mechanica, 19, 23-32 (1974).
  22. C. Rogers, S.P. Castell and J.G. Kingston, On Invariance Properties of Conservation Laws in Non Dissipative Planar Magneto-Gasdynamics, J. de Mécanique, 13, 343-354 (1974).
  23. C. Rogers and D.L. Clements, On the Reduction of the Hodograph Equations for One Dimensional Elastic Plastic Wave Propagation, Quart. Appl. Math., 37, 469-474 (1975).
  24. C. Rogers, Iterated Bäcklund-type Transformations and the Propagation of Disturbances in Non Linear Elastic Materials, J. Math. Anal. Appl., 49, 638-648 (1975).
  25. J.G. Kingston and C. Rogers, On Non-Linear Equations Amenable to the Inverse Scattering Method, Can. J. Phys., 53, 58-61 (1975).
  26. C. Rogers, Invariance and Reducibility Properties under a Class of (m,2)-Bäcklund Transformations, Soc. Ind. Appl. Math. Journal on Applied Mathematics, 28, 11-23 (1975).
  27. K.W. Bauer and C. Rogers, Zur infinitesimalen Deformation von Flächen, Mathematische Statistiche Sektion Forschungszentrum Graz, 31, 1-15 (1975).
  28. C. Rogers and J.J. Swetits, On a Class of Non Linear Filtration Laws, Rheologica Acta, 14, 842-849 (1975).
  29. D.L. Clements and C. Rogers, On the Theory of Stress Concentration for Shear Strained Prismatical Bodies with a Non Linear Stress Strain Law, Mathematika, 22, 34-42 (1975).
  30. C. Rogers, On Applications of Generalised Bäcklund Transformations in Continuum Mechanics, in Bäcklund Transformations, the Inverse Scattering Method and Their Applications, Lecture Notes in Mathematics, 515, 40-68, Springer Verlag, Berlin, (1976) (Ed. R. M. Miura).
  31. T.B. Moodie, C. Rogers and D.L. Clements, Large Wave-length Pulse Propagation in Curved Elastic Rods, J. Acoustical Soc. Amer., 59, 557-563 (1976).
  32. C. Rogers and J.G. Kingston, Reciprocal Properties in Quasi-One Dimensional Oblique Field Magneto-Gasdynamics, J. de Mécanique, 15, 185-192 (1976).
  33. C. Rogers, D.L. Clements and T.B. Moodie, Les ondes de cisaillement a symetrie sphérique en (I+1) dimensions pour un materiau viscoelastique inhomogène et isotropique, Utilitas Mathematica, 10, 167-177 (1976).
  34. T.B. Moodie, C. Rogers and D.L. Clements, Radial Propagation of Axial Shear Waves in an Incompressible Elastic Solid under Finite Deformation, Int. J. Eng. Sci., 14, 585-603 (1976).
  35. H. Rasmussen and C. Rogers, A Note on a New Expansion for the Stefan problem, Letters in Heat and Mass Transfer, 3, 327-332 (1976).
  36. C. Rogers, T.B. Moodie and D.L. Clements, Radial Propagation of Rotary Shear Waves in an Initially Stressed Neo-Hookean Material, J. de. Mécanique, 15, 595-614 (1976).
  37. C. Rogers, H.M. Cekirge and A. Askar, Electromagnetic Wave Propagation in Non Linear Dielectric Media, Acta Mechanica, 26, 59-73 (1977).
  38. C. Rogers and H.M. Cekirge, Non-Linear Dielectrics, Computers and Mathematics with Applications, 3, 105-112 (1977).
  39. C. Rogers, D.L. Clements and T.B. Moodie, Transient Displacement and Stress in Non-Homogeneous Elastic Shells, J. Elasticity, 7, 171-184 (1977).
  40. H.M. Cekirge and C. Rogers, On Elastic-Plastic Wave Propagation; Transmission of Elastic-Plastic Boundaries, Archives of Mechanics, 29, 125-141 (1977).
  41. D.L. Clements and T.B. Moodie and C. Rogers, On the Propagation of Waves from Spherical and Cylindrical Cavities in Anisotropic Materials, Int. J. Eng. Sci., 15, 429-445 (1977).
  42. J.J. Swetits and C. Rogers, On Complementary Extremum Principles, J. Math. Anal. Appl., 62, 445-452 (1978).
  43. D.W. Barclay, T.B. Moodie and C. Rogers, Cylindrical Impact Waves in Inhomogeneous Maxwellian Visco-elastic Media, Acta Mechanica, 29, 93-117 (1978).
  44. D.L. Clements, C. Atkinson and C. Rogers, Anti-Plane Crack Problems for an Inhomogeneous Elastic Material, Acta Mechanica, 29, 199-211 (1978).
  45. D.L. Clements and C. Rogers, On the Bergman Operator Method and Anti-Plane Contact Problems involving an Inhomogeneous Half-Space, Soc. Ind. Appl. Math. J. on Applied Mathematics, 34, 764-773 (1978).
  46. C. Rogers and D.L. Clements, Bergman's Integral Operator Method in Inhomogeneous Elasticity, Quart. Appl. Math., 36, 315-321 (1978).
  47. H. Rasmussen and C. Rogers, Solution of Free Surface Problems using a Rayleigh-Ritz Procedure, in Information Linkage between Applied Mathematics and Industry, Academic Press, 357-364 (1979).
  48. C. Rogers and D.L. Clements, Thermal Stress in Layered Anisotropic Elastic Half Space, Archives of Mechanics, 31, 585-590 (1979).
  49. C. Rogers and J.A. Baker, The Finite Elastodynamics of Hyperelastic Thin Tubes, Int. J. Non Linear Mechanics, 15, 225-233 (1980).
  50. C. Rogers, J.G. Kingston and W.F. Shadwick, On Reciprocal-Type Invariant Transformations in Magneto Gasdynamics, J. Math. Phys., 21, 395-397 (1980).
  51. C. Rogers and J.A. Baker, Invariance Properties under a Reciprocal Bäcklund Transformation in Gasdynamics, J. Mécanique, Théorique et Appliquée, 1, 563-578 (1982).
  52. J.G. Kingston and C. Rogers, Reciprocal Bäcklund Transformations of Conservation Laws, Phys. Lett. 92A, 261-264 (1982).
  53. D.L. Clements and C. Rogers, A Boundary Integral Equation for the Solution of Class of Problems in Anisotropic Inhomogeneous Thermostatics and Elastostatics, Quart. Appl. Math., 41, 99-105 (1983).
  54. C. Rogers, M.P. Stallybrass and D.L. Clements, On Two Phase Filtration under Gravity and with Boundary Infiltration: Application of a Bäcklund Transformation, J. Nonlinear Analysis, Theory, Methods and Applications, 7, 785-799 (1983).
  55. C. Rogers, Application of Reciprocal Bäcklund Transformations to a Class of Nonlinear Boundary Value Problems, J. Phys. A: Mathematical and General, 16, L493-L495 (1983).
  56. C. Rogers, Fokker-Planck Equations Chain Reducible to Canonical Form via Bäcklund Transformations, Phys. Lett. 99A, 136-142 (1983).
  57. C. Rogers, H. Rasmussen and M.P. Stallybrass, Application of a Bäcklund Transformation in Gravity-Driven Two Phase Filtration, Int. J. Multiphase Flow, 10, 95-106 (1984).
  58. J.G. Kingston and C. Rogers, Bäcklund Transformations for Systems of Conservation Laws, Quart. Appl. Math., 51, 423-432 (1984).
  59. J.G. Kingston, C. Rogers and D. Woodall, Reciprocal Auto-Bäcklund Transformations, J. Phys. A: Mathematical and General, 17, L35-L38 (1984).
  60. C. Rogers and P. Wong, On Reciprocal Bäcklund Transformations of Inverse Scattering Schemes, Physica Scripta, 30, 10-14 (1984).
  61. C. Rogers, The Large Amplitude Elastodynamics of Transversely Isotropic Incompressible Hyperelastic Cylinders, Advances in Nonlinear Waves, 1, 184-196, Pitman, Boston, London (1984).
  62. D.L. Clements, D.L. Hill, C. Rogers and J. Mazumdar, On Some Boundary Value Problems in Anisotropic Inhomogeneous Thermostatics and Elastostatics, Soc. Ind. Appl. Math. J. Appl. Math., 44, 969-981 (1984).
  63. C. Rogers, Inverse Transformations and the Reduction of Nonlinear Dirichlet Problems, J. Phys. A: Mathematical and General, 17, L681-685 (1984).
  64. J.M. Hill and C. Rogers, On an Analogy between Plane Finite Elastic Deformations and Certain Magnetohydrodynamic Flows, Zeit. angew. Math. Phys., 35, 24-33 (1984).
  65. C. Rogers and P.L. Sachdev, The Burgers' Hierarchy: On Nonlinear Initial and Boundary Value Problems, Il Nuovo Cimento, 83B, 127-135 (1984).
  66. C. Rogers and R. Sawatsky, Heat Conduction in an Inhomogeneous Half Space Subject to a Nonlinear Boundary Condition: Application of a Bergman Type Series, Int. J. Eng. Science, 23, 415-424 (1985).
  67. C. Rogers, Application of Linked Bäcklund Transformations to Nonlinear Boundary Value Problems, J. Math. Phys., 26, 393-395 (1985).
  68. C. Rogers, Application of a Reciprocal Transformation to a Two Phase Stefan Problem, J. Phys. A: Mathematical and General, 18, L105-L109 (1985).
  69. C. Rogers and T. Ruggeri, A Reciprocal Bäcklund Transformation: Application to a Nonlinear Hyperbolic Model in Heat Conduction, Lett. Il. Nuovo. Cimento, 44, 289-296 (1985).
  70. C. Rogers, C. McInnis and H. Rasmussen, On a Stefan Problem Involving a Spherical Region: Application of a Bergman-Type Expansion, Applied Mathematics and Computation, 18, 143-154 (1986).
  71. C. Rogers, D.W. Barclay and D.L. Clements, Padé Extension of Bergman Series Solutions to Nonlinear Boundary Value Problems, J. Eng. Math., 20, 145-161 (1986).
  72. C. Rogers, Application of Reciprocal Bäcklund Transformations to Stefan Problems in Nonlinear Heat Conduction, Transactions of the US Army Conference on Applied Mathematics and Computing ARO Report, 86-1, 573-587 (1986).
  73. C. Rogers and M.C. Nucci, On Reciprocal Bäcklund Transformations and the Korteweg-de Vries Hierarchy, Physica Scripta, 33, 289-292 (1986).
  74. C. Rogers, Reciprocal Transformations in 2+1-Dimensions, J. Phys. A: Math. Gen., 49, L491-L496 (1986).
  75. C. Rogers, M.C. Nucci and J.G. Kingston, On Reciprocal Auto-Bäcklund Transformations: Application to a New Nonlinear Hierarchy, Il. Nuovo Cimento, 96, 55-63 (1986).
  76. C. Rogers, On a Class of Moving Boundary Problems in Nonlinear Heat Conduction: Application of a Bäcklund Transformation, Int. J. Nonlinear Mechanics, 21, 249-256 (1986).
  77. C. Rogers and A.J. Bracken, On a Ratio Theorem for a Class of Nonlinear Boundary Value Problems, Quart. Appl. Math., 54, 639-648 (1987).
  78. C. Rogers, The Harry Dym Equation in 2+1 Dimensions: A Reciprocal Link with the Kadomtsev- Petviashvili Equation, Phys. Lett. A120, 15-18 (1987).
  79. C. Rogers and S. Carillo, Bäcklund Charts for the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt Hierarchies, in Nonlinear Evolution Equations and Dynamical Systems, World Scientific Press, Singapore, 57-74 (1987).
  80. C. Rogers, Reciprocal Transformations in 2+1 Dimensions, in Nonlinear Evolution Equations and Dynamical Systems, World Scientific Press, Singapore, 109-124 (1987).
  81. C. Rogers and S. Carillo, On Reciprocal Properties of the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt Hierarchies, Physica Scripta, 36, 865-869 (1987).
  82. C. Rogers and P. Broadbridge, On a Nonlinear Moving Boundary Problem with Heterogeneity: Application of a Bäcklund Transformation, Zeit. angew. Math Phys., 39, 122-128 (1988).
  83. C. Rogers and B. Yu Guo, A Note on the Onset of Melting in a Class of Simple Metals. Condition on the Applied Boundary Flux, Acta Mathematica Scientia, 8, 425-430 (1988).
  84. C. Rogers, Physical Applications of Reciprocal Transformations, in Symmetries and Nonlinear Phenomena, 260-288, World Scientific Press, Singapore (1988) (Eds. D Levi and P Winternitz).
  85. P. Broadbridge, J.H. Knight and C. Rogers, Constant Rate Rainfall Infiltration in a Bounded Profile: Exact Solution of a Nonlinear Model, Soil. Sci. Soc. Am. J., 52, 1526-1533 (1988).
  86. B. Yu Guo and C. Rogers, On the Harry Dym Equation and its Solution, Science in China, 32, 283-295 (1989).
  87. C. Rogers, Elliptic Warm Core Theory: The Pulsrodon, Phys. Lett. 138A, 267-273 (1989).
  88. C. Rogers and U. Ramgulam, A Nonlinear Superposition Principle and Lie Group Invariance: Application in Rotating Shallow Water Theory, Int. J. Nonlinear. Mech., 24, 229-236 (1989).
  89. C. Rogers, Generation of Invariance Theorems for Nonlinear Boundary-Value Problems in Shallow Water Theory: An Application of MACSYMA, Numerical and Applied Mathematics, IMACS Meeting Proceedings, Paris, 69-74 (1989).
  90. D. Levi, M.C. Nucci, C. Rogers and P. Winternitz, Group Theoretical Analysis of a Rotating Shallow Liquid in a Rigid Container, J Phys. A : Mathematical and General, 22, 4743-4767 (1989).
  91. C. Rogers, Bäcklund Transformations in Soliton Theory: A Survey of Results, in Nonlinear Science: Theory and Applications, Manchester University Press, 97-130, (1990) (Ed. A Fordy).
  92. C. Athorne, C. Rogers, U. Ramgulam and A. Osbaldestin, On Linearisation of the Ermakov System, Phys. Lett. 143A, 207-212, (1990).
  93. P. Broadbridge and C. Rogers, Exact Solutions for Vertical Drainage and Redistribution in Soils, J. Eng. Math., 24, 25-43, (1990).
  94. B. Yu Guo, C. Rogers and D. Siegel, Application of Maximum Principles to Boundary Value Problems in Nonlinear Heat Conduction, J. Nonlinear. Analysis, Theory, Methods and Applications, 14, 293-304, (1990).
  95. C. Rogers and D. Levi, Group Invariance of a Neo-Hookean System: Incorporation of Stretch Change, J. Elasticity, 24, 295-300 (1990).
  96. B. Konopelchenko and C. Rogers, On 2+1-Dimensional Nonlinear Systems of Loewner-Type, Phys. Lett. 158A, 391-397 (1991).
  97. B. Konopelchenko and C. Rogers, Bäcklund and Reciprocal Transformations: Gauge Connections, in Nonlinear Equations in Applied Science, Academic Press, New York, 317-362 (1992).
  98. C. Rogers and P. Broadbridge, On Sedimentation in a Bounded Column, Int. J. Nonlinear. Mech., 27, 661-667 (1992).
  99. A. Donato, U. Ramgulam and C. Rogers, The 3+1-Dimensional Monge-Ampère Equation in Discontinuity Wave Theory: Application of a Reciprocal Transformation, Meccanica, 27, 257-262 (1992).
  100. B. Konopelchenko, C. Rogers and U. Ramgulam, Generalized 2+1-Dimensional Loewner Systems: Parametrization and Structure, Proceedings 6th Nonlinear Evolution Equations and Dynamical Systems Meeting, (Eds. M. Boiti, L. Martina and F. Pempinelli), 44-52 (1992).
  101. B. Konopelchenko, W.K. Schief and C. Rogers, The 2+1-Dimensional Sine Gordon System: Its Auto-Bäcklund Transformation, Phys. Lett., 172A, 39-48 (1992).
  102. C. Rogers, On Gasdynamic-Solitonic Connections, Proc. NATO Advanced Research Workshop ‘Applications of Analytic and Geometric Methods to Nonlinear Differential Equations’, Exeter University UK, Kluwer Press, Dordrecht, 217-228 (1993). (Ed. P. Clarkson).
  103. P. Broadbridge and C. Rogers, On a Nonlinear Boundary Value Problem: Application of a Lie-Bäcklund Symmetry, J. Austr. Math. Soc., Ser. B, 34, 318-332 (1993).
  104. W. Oevel and C. Rogers, Gauge Transformations and Reciprocal Links in 2+1-Dimensions. Rev. Math. Phys., 5, 299-330 (1993).
  105. B. Konopelchenko and C. Rogers, On Generalized Loewner Systems: Novel Integrable Equations in 2+1-Dimensions, J. Math. Phys., 34, 214-242 (1993).
  106. C. Rogers, C. Hoenselaers and J.R. Ray, On 2+1-Dimensional Ermakov Systems, J. Phys. A: Mathematical and General, 26, 2625-2633 (1993).
  107. C. Rogers, C. Hoenselaers and U. Ramgulam, Ermakov Structure in 2+1-Dimensional Systems. Canonical Reduction, in ‘Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics’, Kluwer Academic Publishers, Netherlands, 317-328, N.H. Ibragimov et al. (eds), 1993.
  108. C. Rogers, W. Oevel and P. Vassiliou, Invariance under Reciprocal Transformations in 1+1 and 2+1 Dimensions. Proceedings International Meeting on Nonlinear Diffusion Phenomena, Indian Institute of Science, Narosa Publishing House, India, 187-196, (1994), P.L. Sachdev and R.E. Grundy (eds).
  109. M.P. Stallybrass, C. Rogers and W.K. Schief, The 2+1-Dimensional Sawada-Kotera Equation. Associated Initial/Boundary Value Problems and Darboux-Levi Transformation, Proceedings 14th IMACS World Congress, Atlanta USA, 444-447 (1994).
  110. C. Rogers, M.P. Stallybrass and P. Vassiliou, An Invariance of the 2+1-Dimensional Harry Dym Equation: Application to Initial/Boundary Value Problems, Int. J. Nonlinear Mech., 29, 145-154 (1994).
  111. M. Johnston, C. Rogers, W.K. Schief and W.M. Seiler, On Moving Pseudo-Spherical Surfaces: A Generalised Weingarten System, Lie Groups and their Applications, 1, 124-136 (1994).
  112. W.K. Schief and C. Rogers, The Affinsphären Equation. Moutard and Bäcklund Transformations, Inverse Problems, 10, 711-731 (1994).
  113. M. Johnston, C. Rogers and W.K. Schief, Generation of Breather Surfaces. Application of a Classical Bäcklund Transformation, Proceedings 14th IMACS World Congress, Atlanta, USA, 243-246 (1994).
  114. W.K. Schief, C. Rogers and S.P. Tsarev, On a 2+1-Dimensional Darboux System: Integrable and Geometric Connections, Chaos, Solitons and Fractals, 5, 2357-2366 (1995).
  115. W.K. Schief, C. Rogers and M. Johnston, On Hyperbolic Surfaces : Moving Triad and Loewner System Connections, Chaos, Solitons and Fractals, 5, 25-34 (1995).
  116. C. Rogers, W.K. Schief and M.P. Stallybrass, Initial/Boundary Value Problems and Darboux-Levi-Type Transformations Associated with a 2+1-Dimensional Eigenfunction Equation, Int. J. Nonlinear Mech., 30, 223-233 (1995).
  117. C. Rogers and W.K. Schief, Multi-Component Ermakov Systems : Structure and Linearization, J. Math. Anal. Appl., 198, 194-220 (1996).
  118. P. Vassiliou, W.M. Seiler and C. Rogers, Formal Analysis of the Cauchy Problem for a System Associated with the 2+1-Dimensional Krichever-Novikov Equation, Acta Applicandae Mathematicae, 42, 249-265 (1996).
  119. C. Rogers and W.K. Schief, On Generalized Ermakov Systems, Proceedings Nonlinear Physics, Theory and Experiment Meeting, Gallipoli, Italy (1996) 278-285 (Eds. E. Alfinito, M Boiti, L Martina and F. Pempinelli).
  120. W.K. Schief and C. Rogers, On a Laplace Sequence of Nonlinear Integrable Ernst-Type Equations, Algebraic Aspects of Integrable Systems in Memory of Irene Dorfman, Progress in Nonlinear Differential Equations, 26, Birkhäuser (1996) 315-321 (Eds. A. Fokas & I.M. Gelfand).
  121. W.K. Schief and C. Rogers, The Geometry of the LKR System. Application of a Laplace-Darboux Transformation to an Ernst-Type Equation, Proceedings Nonlinear Physics, Theory and Experiment Meeting, Gallipoli, Italy (1996) 305-312.
  122. C. Rogers, B.G. Konopelchenko, M.P. Stallybrass and W.K. Schief, The Nizhnik-Veselov-Novikov Equation. Associated Boundary Value Problems, Int. J. Nonlinear Mech., 31, 441-450 (1996).
  123. C. Rogers, W.K. Schief and A. Bassom, Ermakov Systems with Arbitrary Order and Dimension. Structure and Linearization, J. Phys. A: Math. & Gen., 29, 903-911 (1996).
  124. W.K. Schief and C. Rogers, Integration of Finite Loewner Transformations. Darboux Connections in Proceedings International Meeting on Modern Group Analysis, Theory, Computation and Application, University of Witwatersrand 289-311 (1997).
  125. C. Rogers and W.K. Schief, The Classical Bäcklund Transformation and Integrable Discretisation of Characteristic Equations, Phys. Lett. A 232, 217-223 (1997).
  126. C. Rogers, W.K. Schief and P. Winternitz, Lie Theoretical Generalisation and Discretisation of the Pinney Equation, J. Math. Anal. Appl., 216, 246-264 (1997).
  127. L.K. Antanovskii, C. Rogers and W.K. Schief, A Note on a Capillarity Model and the Nonlinear Schrödinger Equation, J. Phys. A: Math & Gen., 30, L555-L557 (1997).
  128. C. Rogers and W.K. Schief, Intrinsic Geometry of the NLS Equation and its Auto-Bäcklund Transformation, Stud. Appl. Math., 101, 267-287 (1998).
  129. W.K. Schief and C. Rogers, Loewner Transformations. Adjoint and Binary Darboux Connections, Stud. Appl. Math., 100, 391-422 (1998).
  130. C. Rogers, E.V. Ferapontov and W.K. Schief, Reciprocal Transformations of Two-Component Hyperbolic Systems and Their Invariants, J. Math. Anal. Appl., 228, 365-376 (1998).
  131. J.J.C. Nimmo, C. Rogers and W.K. Schief, Termination of Bergman Series. Connection to the Bn Toda System, in Applications of Solitons and Symmetries (Eds M.J. Ablowitz et al), J. Eng. Math., 36, 137-148 (1999).
  132. W.K. Schief and C. Rogers, Binormal Motion of Curves of Constant Curvature and Torsion. Generation of Soliton Surfaces, Proc. Roy. Soc. Lond., A455, 3163-3188 (1999).
  133. C. Rogers, A. Bassom and W.K. Schief, On a Painlevé II Model in Steady Electrolysis: Application of a Bäcklund Transformation, J. Math. Anal. Appl., 240, 367-381 (1999).
  134. C. Rogers and W.K. Schief, The Resonant Nonlinear Schrödinger Equation via an Integrable Capillarity Model, Il Nuovo Cimento, 114, 1409-1412 (1999).
  135. C. Rogers, W.K. Schief and M. Johnston, Bäcklund and His Works. Applications in Soliton Theory, in Geometric Approaches to Differential Equations, Australian Mathematical Society Lecture Notes 15, Cambridge University Press, 16-55 (2000).
  136. W.K. Schief and C. Rogers, Bäcklund Transformations and the Integrable Discretisation of Characteristic Systems, in Proceedings, International Meeting on Integrability and Chaos in Discrete Systems, Brussels (1997) Chaos, Fractals and Solitons 11, 107-113 (2000).
  137. C. Rogers and W.K. Schief, On Geodesic Hydrodynamic Motions. Heisenberg Spin Connections, J. Math. Anal. Appl., 251, 855-870 (2000).
  138. C. Rogers and W.K. Schief, The Classical Geometry of Bäcklund Transformations. Applications in Soliton Theory, International Meeting on Bäcklund and Darboux Transformations, CRM Proceedings and Lecture Notes 29, Amer. Math. Soc. 53-67 (2001).
  139. C. Rogers and W.K. Schief, Infinitesimal Bäcklund Transformations of K-Nets. The 2+1-Dimensional Sinh-Gordon System. International Meeting on Bäcklund and Darboux Transformations, CRM Proceedings and Lecture Notes 29, Amer. Math. Soc. 385-392 (2001).
  140. A.S. Fokas and C. Rogers, On Initial/Boundary Value Problems for Simultaneous Evolution Equations in Three-Dimensions, Stud. Appl. Math., 107, 391-401 (2001).
  141. M.C. Mariani, P. Amster and C. Rogers, Dirichlet and Periodic-Type Boundary Value Problems for Painlevé II, J. Math. Anal. Appl., 265, 1-11 (2002).
  142. C. Rogers, W.K. Schief and W.H. Hui, On Complex-lamellar Motion of a Prim Gas, J. Math. Anal. Appl., 266, 55-69 (2002).
  143. A. Degasperis, C. Rogers and W.K. Schief, Isothermic Surfaces Generated via Darboux-Bäcklund Transformations. Boomeron and Zoomeron Connections, Stud. Appl. Math., 109, 39-65 (2002).
  144. C. Rogers, On the Geometry of Spatial Hydrodynamic Motions. Solitonic Connections, in Proceedings XIth International Conference on Waves and Stability in Continuous Media, 458-470 (2002) (Ed. Roberto Monaco).
  145. C. Rogers and W.K. Schief, On the Equilibrium of Elastic Shell Membranes under Normal Loading. Hidden Integrability, Proc. Roy. Soc. Lond. 459, 2449-2462 (2003).
  146. C. Rogers, W.K. Schief and J. Wylie, Wave Propagation in Ideally Hard Elastic Inhomogeneous Materials associated with Pseudo-Spherical Surfaces, Int. J. Eng. Sci., 41, 1965-1974 (2003).
  147. C. Rogers and W.K. Schief, Novel Integrable Reductions in Nonlinear Continuum Mechanics via Geometric Constraints, J. Math. Phys., 44, 3341-3369 (2003).
  148. C. Rogers and W.K. Schief, The Kinematics of the Planar Motion of Fibre-reinforced Fluids. An Integrable Reduction and Bäcklund Transformation, Theoretical and Mathematical Physics, 137, 1598-1608 (2003).
  149. W.K. Schief and C. Rogers, The Kinematics of Fibre-Reinforced Fluids. An Integrable Reduction, Quart. J. Mech. Appl. Math., 56, 493-512 (2003).
  150. S.Y. Lou, C. Rogers and W.K. Schief, Virasoro Structure and Localised Excitations of the LKR System, J. Math. Phys., 44, 5869-5887 (2003).
  151. P. Amster, M.C. Mariani, C. Rogers and C.C. Tisdell, On Two Point Boundary Value Problems in Multi-Ion Electrodiffusion, J. Math. Anal. Appl., 289, 712-721 (2004).
  152. C. Rogers, Bäcklund Transformations, invited entry Encyclopaedia of Nonlinear Science, Routledge, New York (2004) (Ed. Alwyn Scott).
  153. S.Y. Lou, C. Rogers and W.K. Schief, On a Nonlinear Discretised LKR System: Reductions and Underlying Virasoro Symmetry Algebra, Stud. Appl. Math., 113, 353-380 (2004).
  154. C. Rogers and W.K. Schief, Hidden Integrability in Subsonic Gasdynamics. Reciprocal Vortex Street Generation, Int. J. Eng. Sci., 42, 2065-2078 (2004).
  155. W.K. Schief and C. Rogers, The Da Rios System under a Geometric Constraint. The Gilbarg Problem, J. Geom Phys., 54, 286-300 (2005).
  156. A.S. Fokas, C. Rogers and W.K. Schief, Evolution of Methacrylate Distribution during Wood Saturation. A Nonlinear Moving Boundary Problem, Appl. Math. Lett., 18, 321-328 (2005).
  157. C. Rogers, W.K. Schief, K.W. Chow and C.C. Mak, On Tzitzeica Vortex Streets and Their Reciprocals in Subsonic Gasdynamics, Stud. Appl. Math., 114, 271-283 (2005).
  158. C. Rogers and W.K. Schief, Vortex Trains in Super-Alfvénic Magnetogasdynamics. Application of Reciprocal Bäcklund Transformations, J. Nonlinear Math. Phys, 12 (Supplement 1) 548-564 (2005).
  159. P. Amster, C. Rogers and C.C. Tisdell, Existence of Solutions to Dynamic Systems of Equations on Time Scales, J. Math. Anal. Appl., 308, 565-577 (2005).
  160. W.K. Schief, M. Kléman and C. Rogers, On a Nonlinear Elastic Shell System in Liquid Crystal Theory: Generalised Willmore Surfaces and Dupin Cyclides, Proc. Roy. Soc. Lond. A 461, 2817-2837 (2005).
  161. C. Rogers and W.K. Schief, On Orthogonal Homentropic Magnetogasdynamics in Two Dimensions, Zeit. angew. Math. Mech., 86, 464-473 (2006).
  162. K.W. Chow, C.C. Mak, C. Rogers and W.K. Schief, Doubly-Periodic and Multiple Pole Solutions of the Sinh-Poisson Equation: Application of Reciprocal Transformations in Subsonic Gasdynamics, J. Computational & Applied Mathematics, 190, 114-126 (2006).
  163. C. Rogers, W.K. Schief and A. Szereszewski, On a Nonlinear Shell Membrane System: Generalised Cyclide Geometries, Euromech Colloquium 483, Geometrically Non-linear Vibrations of Structures, 45-47 (2007).
  164. J.H. Lee, O.K. Pashaev, C. Rogers and W.K. Schief, The Resonant Nonlinear Schrödinger Equation in Cold Plasma Physics. Application of Backlund Transformations and Superposition Principles, J. Plasma. Phys., 73, 257-272 (2007).
  165. A. Mentrelli, C. Rogers, T. Ruggeri and W.K. Schief, On Two-Pulse and Shock Evolution in a Class of Ideally Hard Elastic Materials, Proceedings of Workshop on Asymptotic Methods in Nonlinear Wave Phenomena, Mondello, Italy, 132-143 (2007) (Ed. Tommaso Ruggeri).
  166. P. Amster and C. Rogers, On Boundary Value Problems in Three-Ion Electrodiffusion, J. Math. Anal. Appl., 333, 42-51 (2007).
  167. C. Rogers, W.K. Schief and K.W. Chow, On a Novel Class of Model Constitutive Laws in Nonlinear Elasticity. Construction via Loewner Theory, Theoretical and Mathematical Physics, 152, 711-720 (2007).
  168. W.K. Schief, A. Szereszewski and C. Rogers, The Lamé Equation in Shell Membrane Theory, J. Math Phys., 48, 073510-073533 (2007).
  169. W.K. Schief, C. Rogers and S. Murugesh, On the Kinematics of 2+1-Dimensional Motions of a Fibre-Reinforced Fluid. Integrable Connections, Quart. J. Mech. Appl. Math., 60, 49-64 (2007).
  170. C. Rogers, K.W. Chow and R. Conte, On a Capillarity Model and the Davey-Stewartson I System. Quasi Doubly-Periodic Wave Patterns., II Nuovo Cimento B, 122, 105-112 (2007).
  171. R. Conte, C. Rogers and W.K. Schief, Painlevé Structure of a Multi-Ion Electrodiffusion System, J. Phys. A. Mathematical & Theoretical, 40, F1031-F1040 (2007).
  172. A. Mentrelli, C. Rogers and W.K. Schief, On Two-Pulse Interaction in a Class of Model Superelastic Materials, Proceedings XIII International Conference on Waves and Stability in Continuous Media (Ed. Tommaso Ruggeri), 394-405 (2008).
  173. J. Flavin and C. Rogers, Upper Estimates for a Moving Boundary Problem for a Resonant Nonlinear Schrödinger Equation, Studies in Applied Mathematics, 121, 189-198 (2008).
  174. D.W.C. Lai, K.W. Chow, C. Rogers and Z. Yan, Anti-Dark Solitons of the Resonant Nonlinear Schrödinger Equation, in Advances in Nonlinear Waves and Symbolic Computation, Nova Science Publications, 101-110 (2008).
  175. O.K. Pashaev, J.H. Lee and C. Rogers, Soliton Resonances in a Generalized Nonlinear Schrödinger Equation, J. Phys. A. Mathematical & Theoretical, 41, 452001-452009 (2008).
  176. X.Y. Tang, K.W. Chow and C. Rogers, Propagating Wave Patterns for the Resonant Davey-Stewartson System, Chaos, Solitons and Fractals, 42, 2707-2712 (2009).
  177. C. Rogers and W.K. Schief, On a Bernoulli-Integrable Magnetohydrodynamic System, Zeit. angew. Math. Phys., 60, 608-620 (2009).
  178. P. Amster, L. Vicchi and C. Rogers, Boundary Value Problems on the Half-Line for a Generalised Painlevé II Equation, Nonlinear Analysis: Theory, Methods & Applications, 71, 149-154 (2009).
  179. C. Rogers, L.P. Yip and K.W. Chow, A Resonant Davey-Stewartson Capillarity Model System. Soliton Generation, International Journal of Nonlinear Sciences and Numerical Simulation, 10, 397-405 (2009).
  180. W.K. Schief, A. Szereszewski and C. Rogers, On Shell Membranes of Enneper-type: Generalised Dupin Cyclides, in Nonlinearity and Geometry: Connections with Integrability, J. Phys. A. Mathematical & Theoretical 42, 40415 (12 pp) (2009).
  181. C. Rogers and A. Szereszewski, A Bäcklund Transformation for L-Isothermic Surfaces, in Nonlinearity and Geometry: Connections with Integrability, J. Phys. A. Mathematical & Theoretical 42, 404016 (17 pp) (2009).
  182. C. Rogers and W.K. Schief, Bäcklund Transformations and Superposition Principles in Nonlinear Elastodynamics, Stud. Appl. Math. 124, 137-149 (2010).
  183. W.K. Schief and C. Rogers, Modulated Waves and Helicoidal Pseudo-spherical Surfaces in Nonlinear Inhomogeneous Elasticity, J. Phys. A. Mathematical & Theoretical 43, 105206 (12pp) (2010).
  184. C. Rogers and W.K. Schief, Integrable Structure in the Theory of Stress Concentration in Shear-Strained Elastic Materials, Stud. Appl. Math. 125, 39-53 (2010).
  185. L.K. Bass, J. Nimmo, C. Rogers and W.K. Schief, Electrical Structures of Interfaces. A Painlevé II Model, Proc. Roy. Soc. LondonA 466, 2117-2136 (2010).
  186. C. Rogers, W.K. Schief, A. Mentrelli and T. Ruggeri, Application of a Bäcklund Transformation in Nonlinear Elastodynamics: Two Pulse Interaction, Proceedings XV International Conference on Waves and Stability in Continuous Media, Palermo, Italy, 260-269 (2010).
  187. C. Rogers, W.K. Schief and A. Szereszewski, Loop Soliton Interaction in an Integrable Nonlinear Telegraphy Model. Reciprocal and Bäcklund Transformations, J. Phys. A Mathematical & Theoretical 43, 385210 (16 pp) (2010).
  188. C. Rogers and H. An, Ermakov-Ray-Reid Systems in 2+1-Dimensional Rotating Shallow Water Theory, Stud. Appl. Math. 125, 275-299 (2010).
  189. C. Rogers, On a Ermakov-Ray-Reid reduction in 2+1-Dimensional Transverse Magnetogasdynamics, Proceedings International Workshop on Group Analysis and Integrable Systems, Cyprus (2010).
  190. C. Rogers, B. Malomed, K.W. Chow and H. An, Ermakov-Ray-Reid Systems in Nonlinear Optics, J. Phys. A Mathematical & Theoretical 43, 455214 (15pp) (2010).
  191. P. Amster, M.K. Kwong and C. Rogers, On a Neumann Boundary Value Problem for Painlevé II in Two-Ion Electro-diffusion, Nonlinear Analysis: Theory, Methods & Applications 74, 2897-2907(2011).
  192. C. Rogers and O.K. Pashaev, on a 2+1-Dimensional Whitham-Broer-Kaup System. A Resonant NLS Connection, to be published, Stud. Appl. Math. (2011).
  193. C. Rogers, On 2+1-Dimensional Magnetohydrodynamics with a Constant Divergence Constraint, to be published, Proceedings, International Meeting on Nonlinear Evolution Equations and Materials with Memory, La Sapienza Press, Universita di Roma (2011).
  194. C. Rogers and A. Szereszewski, On the Geometry of Complex-lamellar Magnetohydrodynamics. Universal Motions, to be published, Stud. Appl. Math.(2011).
  195. C. Rogers and W.K. Schief, The Pulsrodon in 2+1-Dimensional Magnetogasdynamics. Hamiltonian-Ermakov Reduction, submitted.
  196. C. Rogers and H. An, On a 2+1-Dimensional Madelung System with Logarithmic and de Broglie-Bohm Quantum Potentials. Ermakov Reduction, submitted.
  197. P. Amster, M.K. Kwong and C. Rogers, A Neumann Boundary Value Problem in Two-Ion Electro-diffusion, submitted.
  198. C. Rogers and W.K. Schief, On the integrability of a 2+1-Dimensional Non-Isothermal Rotating Gas Cloud System, submitted.
  199. C. Rogers and W.K. Schief, A Non-Isothermal Spinning Magnetogasdynamic Cloud System. Integrable and Hamiltonian- Ermakov Structure, in preparation.
  200. C. Rogers, B. Malomed and H. An, On a 3+1-Dimensional Modulated NLS Equation. Ermakov-Ray-Reid Reductions of a Variational Approximation, in preparation.