143 citations · 359 across the 7 of their papers we have counts for
7 papers
Evolution of wind-generated shallow water waves in a Benney-Luke equation
Montri Maleewong, Roger Grimshaw
In recent papers, denoted by MG24, MG25 in this text, we used the Korteweg-de Vries (KdV) equation and its two-dimensional extension, the Kadomtsev-Petviashvili (KP) equation to de…
Decay of Kadomtsev - Petviashvili lumps in dissipative media
S. Clarke, K. Gorshkov, R. Grimshaw +1
The decay of Kadomtsev - Petviashvili lumps is considered for a few typical dissipations - Rayleigh dissipation, Reynolds dissipation, Landau damping, Chezy bottom friction, viscou…
Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation
A. M. Kamchatnov, Y. -H. Kuo, T. -C. Lin +5
Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or G…
Undular bore theory for the Gardner equation
A. M. Kamchatnov, Y. -H. Kuo, T. -C. Lin +5
We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg--de Vries, equation, which is a generic mathematical m…
Unsteady undular bores in fully nonlinear shallow-water theory
G. A. El, R. H. J. Grimshaw, N. F. Smyth
We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the lead…
Analytic model for a frictional shallow-water undular bore
G. A. El, R. H. J. Grimshaw, A. M. Kamchatnov
We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is ma…