On Whitham theory for perturbed integrable equations

Abstract

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times 2$ matrix or second order scalar spectral problems. The theory is illustrated by derivation of the Whitham equations for perturbed Korteweg-de Vries equation and nonlinear Schrödinger equation with linear damping.

17 pages, no figures

References in corpus (2)

• Formation and Propagation of Matter Wave Soliton Trains
• Adiabatic dynamics of periodic waves in Bose-Einstein condensate with time dependent atomic scattering length

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