32 citations · 65 across the 10 of their papers we have counts for
10 papers
Reappraisal of Whitham's 1967 theory for wave-mean flow interaction in shallow water
Thomas J. Bridges, Daniel J. Ratliff
The modulation equations for Stokes waves in shallow water coupled to wave generated mean flow, derived in Whitham (1967), based on an averaged Lagrangian are revisited. Firstly, i…
The Kawahara Equation: Traveling Wave Solutions Joining Periodic Waves
Patrick Sprenger, Thomas J. Bridges, Michael Shearer
The Kawahara equation is a weakly nonlinear long-wave model of dispersive waves that emerges when leading order dispersive effects are in balance with the next order correction. Tr…
Validity of the hyperbolic Whitham modulation equations in Sobolev spaces
Thomas J. Bridges, Anna Kostianko, Sergey Zelik
It is proved that modulation in time and space of periodic wave trains, of the defocussing nonlinear Schrödinger equation, can be approximated by solutions of the Whitham modulatio…
Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory
Thomas J. Bridges, Daniel J. Ratliff
The multiphase Whitham modulation equations with phases have characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for…
Regularizing the Cross-Newell equation by re-modulating along a characteristic angle
Nicholas J Burgess, Thomas J Bridges
A regularization of the Cross-Newell equation is presented. It is based on a secondary re-modulation along characteristics. This new characteristic Cross-Newell equation is not iso…
A proof of validity for multiphase Whitham modulation theory
Tom Bridges, Anna Kostianko, Guido Schneider
It is proved that approximations which are obtained as solutions of the multiphase Whitham modulation equations stay close to solutions of the original equation on a natural time s…