47 citations · 181 across the 13 of their papers we have counts for
13 papers
Amplification of wave groups in the forced nonlinear Schrödinger equation
Montri Maleewong, Roger Grimshaw
In many physical contexts, notably including deep water waves, modulation instability in one space dimension is often studied using the nonlinear Schrödinger equation. The principa…
Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current
Curtis Hooper, Karima Khusnutdinova, Roger Grimshaw
We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear flow. The far-field modal and amplitude equations for the ring waves are prese…
Interaction of internal solitary waves with long waves within the rotation modified Benjamin-Ono equation
R. H. J. Grimshaw, N. F. Smyth, Y. A. Stepanyants
Interaction of a solitary wave with a long background wave is studied within the framework of rotation modified Benjamin-Ono equation describing internal waves in a deep fluid. Wit…
Quartet, higher order and near resonant interactions in nonlinear wave equations
Alex Owen, Roger Grimshaw, Beth Wingate
Motivated by problems arising in geophysical fluid dynamics, we investigate resonant and near resonant wave interactions in nonlinear wave equations with quadratic nonlinearity, We…
Fast and slow resonant triads in the two layer rotating shallow water equations
Alex Owen, Roger Grimshaw, Beth Wingate
In this paper we examine triad resonances in a rotating shallow water system when there are two free interfaces. This allows for an examination in a relatively simple model of the…
Decay of Benjamin - Ono solitons under the influence of dissipation
Roger H. Grimshaw, Noel F. Smyth, Yury A. Stepanyants
The adiabatic decay of Benjamin - Ono algebraic solitons is studied when the influence of various types of small dissipation and radiative losses due to large scale Coriolis disper…
Coupled Ostrovsky equations for internal waves in a shear flow
A. Alias, R. H. J. Grimshaw, K. R. Khusnutdinova
In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rota…
Dynamics of rogue waves on a multi-soliton background in a vector nonlinear Schrodinger equation
Gui Mu, Zhenyun Qin, Roger Grimshaw
General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method…
Global existence of small-norm solutions in the reduced Ostrovsky equation
Roger Grimshaw, Dmitry Pelinovsky
We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitzéica equation and prove global existence of small-norm solutions in Sobolev space . T…
Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory
G. A. El, R. H. J. Grimshaw, N. F. Smyth
We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value…
Modulational instability of two pairs of counter-propagating waves and energy exchange in two-component media
S. D. Griffiths, R. H. J. Grimshaw, K. R. Khusnutdinova
The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We co…
Cuspons, peakons and regular gap solitons between three dispersion curves
Roger Grimshaw, Boris A. Malomed, Georg A. Gottwald
A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence…
"Dispersion management" for solitons in a Korteweg-de Vries system
Simon Clarke, Boris A. Malomed, Roger Grimshaw
The existence of ``dispersion-managed solitons'', i.e., stable pulsating solitary-wave solutions to the nonlinear Schrödinger equation with periodically modulated and sign-variable…