47 citations · 181 across the 13 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…