1 citations · 1 across the 3 of their papers we have counts for
6 papers
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…
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…
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…