19 citations · 57 across the 6 of their papers we have counts for
6 papers
Exponential and algebraic decaying solitary waves and their connection to hydraulic fall solutions
Keith C. H. Chan, Andrew C. Cullen, Simon R. Clarke
The forced Korteweg-de Vries (fKdV) equation describes incompressible inviscid free surface flows over some arbitrary topography. We investigate solitary and hydraulic fall solutio…
A Fast, Spectrally Accurate Homotopy Based Numerical Method For Solving Nonlinear Differential Equations
Andrew C. Cullen, Simon R. Clarke
We present an algorithm for constructing numerical solutions to one--dimensional nonlinear, variable coefficient boundary value problems. This scheme is based upon applying the Hom…
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…
"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…
An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg-de Vries Solitons
P. D. Miller, S. R. Clarke
Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a li…
Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schrödinger equation
S. R. Clarke, R. H. J. Grimshaw, Boris A. Malomed
We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocussing region into a focussing one in a spatially inhomogeneous nonlinear waveguide,…