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 soliton gas.
|Number of pages||10|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Early online date||8 Apr 2003|
|Publication status||Published - 19 May 2003|