Roger Grimshaw

Articles in Scholarly Journals [Incomplete List]

  1. Solitary wave solution for a non-integrable, variable coefficient nonlinear Schrödinger equation
    Physica Scripta, vol. 75, no. 5, pp. 620–623, 2007
  2. Rossby Solitary Waves in the Presence of a Critical Layer
    Studies in Applied Mathematics, vol. 118, no. 4, pp. 313–364, 2007
  3. Novel Solitary Pulses for a Variable-Coefficient Derivative Nonlinear Schrödinger Equation
    Journal of the Physical Society of Japan, vol. 76, no. 7, p. 074004, 2007
  4. Modelling internal solitary waves on the Australian North West Shelf
    Marine and Freshwater Research, vol. 57, no. 3, p. 265, 2006
  5. Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system
    Physica D: Nonlinear Phenomena, vol. 214, no. 1, pp. 1–24, 2006
  6. Unsteady undular bores in fully nonlinear shallow-water theory
    Physics of Fluids, vol. 18, no. 2, p. 027104, 2006
  7. Analytic model for a weakly dissipative shallow-water undular bore
    Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 15, no. 3, p. 037102, 2005
  8. Soliton dynamics in a strong periodic field: The Korteweg–de Vries framework
    Physics Letters A, vol. 344, no. 2-4, pp. 203–210, 2005
  9. Generalized solitary waves and fronts in coupled Korteweg–de Vries systems
    Physica D: Nonlinear Phenomena, vol. 210, no. 1-2, pp. 96–117, 2005
  10. Frictional effects on the deep-flow feedback on the -drift of a baroclinic vortex over sloping topography
    Deep Sea Research Part I: Oceanographic Research Papers, vol. 52, no. 11, pp. 2156–2167, 2005
  11. Interactions of breathers and solitons in the extended Korteweg–de Vries equation
    Wave Motion, vol. 43, no. 2, pp. 158–166, 2005
  12. Free surface flow under gravity and surface tension due to an applied pressure distribution: I Bond number greater than one-third
    Theoretical and Computational Fluid Dynamics, vol. 19, no. 4, pp. 237–252, 2005
  13. Free surface flow under gravity and surface tension due to an applied pressure distribution II Bond number less than one-third
    European Journal of Mechanics - B/Fluids, vol. 24, no. 4, pp. 502–521, 2005
  14. Short-Lived Large-Amplitude Pulses in the Nonlinear Long-Wave Model Described by the Modified Korteweg-De Vries Equation
    Studies in Applied Mathematics, vol. 114, no. 2, pp. 189–210, 2005
  15. Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System
    Studies in Applied Mathematics, vol. 114, no. 4, pp. 395–411, 2005
  16. Rossby Waves on a Shear Flow with Recirculation Cores
    Studies in Applied Mathematics, vol. 115, no. 4, pp. 387–403, 2005
  17. Comments on “On Internal Waves in a Lagrangian Reference Frame”
    Journal of the Atmospheric Sciences, vol. 62, no. 1, p. 251, 2005
  18. Reply
    Journal of the Atmospheric Sciences, vol. 62, no. 1, p. 254, 2005
  19. Internal Waves in a Lagrangian Reference Frame
    Journal of the Atmospheric Sciences, vol. 61, no. 11, p. 1308, 2004
  20. Generation of Secondary Solitary Waves in the Variable-Coefficient Korteweg-de Vries Equation
    Studies in Applied Mathematics, vol. 112, no. 3, pp. 271–279, 2004
  21. The Effect of Bubbles on Internal Waves
    Journal of Physical Oceanography, vol. 34, no. 2, p. 477, 2004
  22. Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves
    Journal of Physical Oceanography, vol. 34, no. 12, p. 2774, 2004
  23. Steady multipolar planar vortices with nonlinear critical layers
    Geophysical & Astrophysical Fluid Dynamics, vol. 98, no. 6, pp. 473–506, 2004
  24. Internal waves in a three-layer bubbly waveguide
    Deep Sea Research Part II: Topical Studies in Oceanography, vol. 51, no. 25-26, pp. 2905–2917, 2004
  25. Interaction of two lump solitons described by the Kadomtsev–Petviashvili I equation
    Wave Motion, vol. 40, no. 2, pp. 123–135, 2004
  26. Damping of large-amplitude solitary waves
    Wave Motion, vol. 37, no. 4, pp. 351–364, 2003
  27. Solitary waves of a coupled Korteweg-de Vries system
    Mathematics and Computers in Simulation, vol. 62, no. 1-2, pp. 31–40, 2003
  28. Theoretical and Mathematical Physics, vol. 137, no. 1, pp. 1448–1458, 2003
  29. The effect of barriers on the tidal range in estuaries
    Estuarine, Coastal and Shelf Science, vol. 58, no. 1, pp. 57–66, 2003
  30. Nonlinear geostrophic adjustment in the presence of a boundary
    Journal of Fluid Mechanics, vol. 471, pp. 257–283, 2002
  31. Dispersion management for solitons in a Korteweg–de Vries system
    Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 12, no. 1, p. 8, 2002
  32. Generation of large-amplitude solitons in the extended Korteweg–de Vries equation
    Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 12, no. 4, p. 1070, 2002
  33. Generation of undular bores in the shelves of slowly-varying solitary waves
    Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 12, no. 4, p. 1015, 2002
  34. Solitary waves with recirculation zones in axisymmetric rotating flows
    Journal of Fluid Mechanics, vol. 464, pp. 217–250, 2002
  35. The effect of a barrier on tidally forced flow in a density-stratified estuary
    Continental Shelf Research, vol. 22, no. 14, pp. 2035–2044, 2002
  36. Transcritical flow of a stratified fluid: The forced extended Korteweg–de Vries model
    Physics of Fluids, vol. 14, no. 2, p. 755, 2002
  37. Singular and regular gap solitons between three dispersion curves
    Physical Review E, vol. 65, no. 6, 2002
  38. Long-Wave Instability in a Three-Layer Stratified Shear Flow
    Studies in Applied Mathematics, vol. 108, no. 1, pp. 77–88, 2002
  39. International Journal of Bifurcation and Chaos [in Applied Sciences and Engineering], vol. 12, no. 11, p. 2409, 2002
  40. Transient Linear Growth and Nonlinear Effects
    Studies in Applied Mathematics, vol. 106, no. 1, pp. 47–68, 2001
  41. Ageostrophic dynamics of an intense localized vortex on a β-plane
    Journal of Fluid Mechanics, vol. 443, pp. 351–376, 2001
  42. Integrable Shallow-Water Equations and Undular Bores
    Studies in Applied Mathematics, vol. 106, no. 2, pp. 157–186, 2001
  43. Short-Wave Instability in a Three-Layer Stratified Shear Flow
    The Quarterly Journal of Mechanics and Applied Mathematics, vol. 54, no. 3, pp. 375–388, 2001
  44. Numerical simulations of the flow of a continuously stratified fluid, incorporating inertial effects
    Fluid Dynamics Research, vol. 28, no. 5, pp. 323–347, 2001
  45. The two-parameter soliton family for the interaction of a fundamental and its second harmonic
    Physica D: Nonlinear Phenomena, vol. 152-153, no. 1-2, pp. 325–339, 2001
  46. Wave group dynamics in weakly nonlinear long-wave models
    Physica D Nonlinear Phenomena, vol. 159, no. 1-2, pp. 35–57, 2001
  47. On the long-term evolution of an intense localized divergent vortex on the beta-plane
    Journal of Fluid Mechanics, vol. 422, pp. 249–280, 2000
  48. Weakly nonlinear internal wave fronts trapped in contractions
    Journal of Fluid Mechanics, vol. 415, pp. 323–345, 2000
  49. On the generation of solitons and breathers in the modified Korteweg–de Vries equation
    Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 10, no. 2, p. 383, 2000
  50. The effect of weak shear on finite-amplitude internal solitary waves
    Journal of Fluid Mechanics, vol. 395, pp. 125–159, 1999
  51. Solitary waves in a two-layer quasigeostrophic model with wind stress forcing
    Geophysical & Astrophysical Fluid Dynamics, vol. 91, no. 3, pp. 169–197, 1999
  52. Journal of Engineering Mathematics, vol. 36, no. 1/2, pp. 89–98, 1999
  53. Hamiltonian-versus-energy diagrams in soliton theory
    Physical Review E, vol. 59, no. 5, pp. 6088–6096, 1999
  54. The Formation of Coherent Structures in the Context of Blocking
    Journal of the Atmospheric Sciences, vol. 56, no. 21, pp. 3640–3662, 1999
  55. The Effect of Topography on the Dynamics of Interacting Solitary Waves in the Context of Atmospheric Blocking
    Journal of the Atmospheric Sciences, vol. 56, no. 21, pp. 3663–3678, 1999
  56. Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity
    Physica D: Nonlinear Phenomena, vol. 132, no. 1-2, pp. 40–62, 1999
  57. Dissipative effects in a nonlinear wave system with an unstable linear spectrum
    Physica D: Nonlinear Phenomena, vol. 132, no. 1-2, pp. 63–86, 1999
  58. Numerical simulations of internal solitary waves with vortex cores
    Fluid Dynamics Research, vol. 25, no. 6, pp. 315–333, 1999
  59. Adjustment processes and radiating solitary waves in a regularised ostrovsky equation
    European Journal of Mechanics - B/Fluids, vol. 18, no. 3, pp. 535–543, 1999
  60. Exact periodic steady solutions for nonlinear wave equations: A new approach
    Physics Letters A, vol. 251, no. 1, pp. 25–30, 1999
  61. Passage of a wave pulse through a zero-dispersion point in the nonlinear Schrödinger equation
    Physics Letters A, vol. 262, no. 6, pp. 434–444, 1999
  62. Stable two-dimensional parametric solitons in fluid systems
    Physics Letters A, vol. 248, no. 2-4, pp. 208–218, 1998
  63. Nonlinear analysis of instability produced by linear mode coupling
    Physica D: Nonlinear Phenomena, vol. 113, no. 1, pp. 26–42, 1998
  64. The effect of the induced mean flow on solitary waves in deep water
    Journal of Fluid Mechanics, vol. 355, pp. 317–328, 1998
  65. Terminal Damping of a Solitary Wave Due to Radiation in Rotational Systems
    Studies in Applied Mathematics, vol. 101, no. 2, pp. 197–210, 1998
  66. Solitary Wave Transformation Due to a Change in Polarity
    Studies in Applied Mathematics, vol. 101, no. 4, pp. 357–388, 1998
  67. Instability analysis of internal solitary waves in a nearly uniformly stratified fluid
    Physics of Fluids, vol. 9, no. 11, p. 3343, 1997
  68. Solitary waves with a vortex core in a shallow layer of stratified fluid
    Physics of Fluids, vol. 9, no. 11, p. 3378, 1997
  69. On basic mechanisms governing two-layer vortices on a β-plane
    Geophysical & Astrophysical Fluid Dynamics, vol. 86, no. 1, pp. 1–42, 1997
  70. Transformation of a soliton at a point of zero nonlinearity
    Journal of Experimental and Theoretical Physics Letters, vol. 65, no. 1, pp. 120–125, 1997
  71. International Journal of Bifurcation and Chaos [In Applied Sciences and Engineering], vol. 7, no. 12, p. 2653, 1997
  72. Parametric envelope solitons in coupled Korteweg-de Vries equations
    Physics Letters A, vol. 227, no. 1-2, pp. 47–54, 1997
  73. Structural transformation of eigenvalues for a perturbed algebraic soliton potential
    Physics Letters A, vol. 229, no. 3, pp. 165–172, 1997
  74. Hysteresis phenomena in the interaction of a damped solitary wave with an external force
    Wave Motion, vol. 26, no. 3, pp. 253–274, 1997
  75. An asymptotic approach to solitary wave instability and critical collapse in long-wave KdV-type evolution equations
    Physica D: Nonlinear Phenomena, vol. 98, no. 1, pp. 139–155, 1996
  76. Dynamics of internal solitary waves in a rotating fluid
    Dynamics of Atmospheres and Oceans, vol. 23, no. 1-4, pp. 403–411, 1996
  77. Radiation Boundary Conditions in Barotropic Coastal Ocean Numerical Models
    Journal of Computational Physics, vol. 123, no. 1, pp. 96–110, 1996
  78. Numerical simulations of uniformly stratified fluid flow over topography
    Journal of Fluid Mechanics, vol. 306, no. -1, p. 1, 1996
  79. Two-dimensional disturbance growth of linearly stable viscous shear flows
    Physics of Fluids, vol. 8, no. 6, p. 1424, 1996
  80. On the asymptotic integrability of a higher-order evolution equation describing internal waves in a deep fluid
    Journal of Mathematical Physics, vol. 37, no. 7, p. 3415, 1996
  81. The effect of wind-wave enhancement of bottom stress on the circulation induced by tropical cyclones on continental shelves
    Journal of Geophysical Research, vol. 101, no. C10, pp. 22705–22714, 1996
  82. SIAM Journal on Applied Mathematics, vol. 55, no. 1, Article ID 0155005, 1995
  83. A spectral transform for the intermediate nonlinear Schrödinger equation
    Journal of Mathematical Physics, vol. 36, no. 8, p. 4203, 1995
  84. International Journal of Bifurcation and Chaos [in Applied Sciences and Engineering], vol. 5, no. 4, p. 1221, 1995
  85. The modulation of nonlinear periodic wavetrains by dissipative terms in the Korteweg-de Vries equation
    Wave Motion, vol. 22, no. 2, pp. 215–238, 1995
  86. Gap-soliton hunt in a coupled Korteweg-de Vries system
    Physics Letters A, vol. 201, no. 4, pp. 285–292, 1995
  87. Nonexistence of gap solitons in nonlinearly coupled systems
    Physics Letters A, vol. 198, no. 3, pp. 205–208, 1995
  88. Solitary waves with damped oscillatory tails: an analysis of the fifth-order Korteweg-de Vries equation
    Physica D: Nonlinear Phenomena, vol. 77, no. 4, pp. 473–485, 1994
  89. Interaction of a solitary wave with an external force
    Physica D: Nonlinear Phenomena, vol. 77, no. 4, pp. 405–433, 1994
  90. Resonant wave interactions near a critical level in a stratified shear flow
    Journal of Fluid Mechanics, vol. 269, no. -1, p. 1, 1994
  91. Resonantly generated internal waves in a contraction
    Journal of Fluid Mechanics, vol. 274, no. -1, p. 139, 1994
  92. New type of gap soliton in a coupled Korteweg–de Vries wave system
    Physical Review Letters, vol. 72, no. 7, pp. 949–953, 1994
  93. Periodic and Chaotic Behaviour in a Reduction of the Perturbed Korteweg-De Vries Equation
    Proceedings of the Royal Society: Mathematical and Physical Sciences (1990-1995), vol. 445, no. 1923, pp. 1–21, 1994
  94. The effect of vortex stretching on the evolution of barotropic eddies over a topographic slope
    Geophysical & Astrophysical Fluid Dynamics, vol. 76, no. 1, pp. 43–71, 1994
  95. Explosive resonant triads in a continuously stratified shear flow
    Journal of Fluid Mechanics, vol. 257, no. -1, p. 219, 1993
  96. The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation
    Physica D: Nonlinear Phenomena, vol. 69, no. 3-4, pp. 270–278, 1993
  97. The generation of edge waves by radiation stress
    Continental Shelf Research, vol. 13, no. 7, pp. 777–802, 1993
  98. The use of Borel-summation in the establishment of non-existence of certain travelling-wave solutions of the Kuramoto-Sivashinsky equation
    Wave Motion, vol. 15, no. 4, pp. 393–395, 1992
  99. Solitary internal waves with oscillatory tails
    Journal of Fluid Mechanics, vol. 242, no. -1, p. 279, 1992
  100. Resonant generation of finite-amplitude waves by the flow of a uniformly stratified fluid over topography
    Journal of Fluid Mechanics, vol. 229, no. -1, p. 603, 1991
  101. The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation
    Physica D: Nonlinear Phenomena, vol. 50, no. 2, pp. 231–238, 1991
  102. Resonant forcing of coastally trapped waves in a continuously stratified ocean
    Pure and Applied Geophysics PAGEOPH, vol. 133, no. 4, pp. 635–664, 1990
  103. Upstream-advancing waves generated by three-dimensional moving disturbances
    Physics of Fluids A: Fluid Dynamics, vol. 2, no. 2, p. 194, 1990
  104. Instability and filamentation of finite-amplitude waves on vortex layers of finite thickness
    Journal of Fluid Mechanics, vol. 209, no. -1, p. 359, 1989
  105. The energetics of the interaction between short small-amplitude internal waves and inertial waves
    Journal of Fluid Mechanics, vol. 196, no. -1, p. 93, 1988
  106. Resonant wave interactions in a stratified shear flow
    Journal of Fluid Mechanics, vol. 190, no. -1, p. 357, 1988
  107. Travelling wave solutions of the Kuramoto-Sivashinsky equation
    Wave Motion, vol. 10, no. 5, pp. 405–420, 1988
  108. Finite-amplitude solitary waves at the interface between two homogeneous fluids
    Physics of Fluids, vol. 31, no. 12, p. 3550, 1988
  109. Stability of finite-amplitude interfacial waves. Part 3. The effect of basic current shear for one-dimensional instabilities
    Journal of Fluid Mechanics, vol. 172, no. -1, p. 277, 1986
  110. Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves
    Journal of Fluid Mechanics, vol. 160, no. -1, p. 297, 1985
  111. Stability of finite-amplitude interfacial waves. Part 2. Numerical results
    Journal of Fluid Mechanics, vol. 160, no. -1, p. 317, 1985
  112. Stable and unstable barotropic shelf waves in a coastal current
    Geophysical & Astrophysical Fluid Dynamics, vol. 29, no. 1, pp. 179–220, 1984
  113. Interfacial progressive gravity waves in a two-layer shear flow
    Physics of Fluids, vol. 26, no. 7, p. 1731, 1983
  114. A second-order theory for solitary waves in shallow fluids
    Physics of Fluids, vol. 26, no. 1, p. 14, 1983
  115. The effect of dissipative processes on mean flows induced by internal gravity-wave packets
    Journal of Fluid Mechanics, vol. 115, no. -1, p. 347, 1982
  116. Modulation of an internal gravity wave packet in a stratified shear flow
    Wave Motion, vol. 3, no. 1, pp. 81–103, 1981
  117. Solitary waves in a compressible fluid
    Pure and Applied Geophysics PAGEOPH, vol. 119, no. 4, pp. 780–797, 1981
  118. Slowly Varying Solitary Waves in Deep Fluids
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), vol. 376, no. 1765, pp. 319–332, 1981
  119. SIAM Journal on Applied Mathematics, vol. 40, no. 1, Article ID 0140002, 1981
  120. A second-order theory for solitary waves in deep fluids
    Physics of Fluids, vol. 24, no. 9, p. 1611, 1981
  121. An Exact Finite-Amplitude Wave on a Helmholtz Velocity Profile in an Infinite Boussinesq Fluid
    Journal of the Atmospheric Sciences, vol. 37, no. 12, pp. 2793–2795, 1980
  122. Mean Flows Induced by Internal Gravity Wave Packets Propagating in a Shear Flow
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), vol. 292, no. 1393, pp. 391–417, 1979
  123. Slowly Varying Solitary Waves. I. Korteweg-De Vries Equation
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), vol. 368, no. 1734, pp. 359–375, 1979
  124. Slowly Varying Solitary Waves. II. Nonlinear Schrodinger Equation
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), vol. 368, no. 1734, pp. 377–388, 1979
  125. On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile
    Journal of Fluid Mechanics, vol. 90, no. 01, p. 161, 1979
  126. Long nonlinear internal waves in channels of arbitrary cross-section
    Journal of Fluid Mechanics, vol. 86, no. 03, p. 415, 1978
  127. Nonlinear internal gravity waves in a rotating fluid
    Journal of Fluid Mechanics, vol. 71, no. 03, p. 497, 1975
  128. SIAM Journal on Applied Mathematics, vol. 19, no. 1, Article ID 0119013, 1970
  129. High-frequency scattering by finite convex regions
    Communications on Pure and Applied Mathematics, vol. 19, no. 2, pp. 167–198, 1966