The thermodynamic limit of the Whitham equations

2003/10/13 by G. A. El · 4 citations
Physics and Astronomy · #nlin.SI #nlin.CD

paper · pdf · doi:10.1016/s0375-9601(03)00515-2

published as Physics Letters A 311 (2003) 374-383

arxiv created 2003/10/13 · arxiv updated 2009/12/01

Abstract

The infinite-genus limit of the KdV-Whitham equations is derived. The limit involves special scaling for the associated spectral surface such that the integrated density of states remains finite as N → ∞ (the thermodynamic type limit). The limiting integro-differential system describes slow evolution of the density of states and can be regarded as the kinetic equation for a soliton gas.

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