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On Whitham theory for perturbed integrable equations

A. M. Kamchatnov
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Abstract

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ 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.

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A. M. Kamchatnov. 2003-02-12. On Whitham theory for perturbed integrable equations. https://doi.org/10.1016/j.physd.2003.07.008

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