32 citations · 65 across the 10 of their papers we have counts for
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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…