arXiv subjects

G. A. El

Publications and source records attributed to G. A. El.

38 records · Page 3Linked to original sources

arXiv2003

The thermodynamic limit of the Whitham equations

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.

nlin.SI↗

arXiv1995

On evolution of multiphase nonlinear modulated waves

We present a fundamental solution to an initial value problem for the KdV-Whitham system in an explicit integral form. Monotonically decreasing initial data with finite number of breaking points are considered. Generating function for the commuting flows of the averaged KdV hieararchy producing the analytical solutions to the KdV-Whitham system is constructed.

solv-int↗