Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-10-13
Physics Letters A 311 (2003) 374-383
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
10.1016/S0375-9601(03)00515-2
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 $N \to \infty$ (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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