The zero dispersion limit for the Korteweg-deVries KdV equation

Abstract

We use the inverse scattering method to determine the weak limit of solutions of the Korteweg-deVries equation as dispersion tends to zero. The limit, valid for all time, is characterized in terms of a quadratic programming problem which can be solved with the aid of function theoretic methods. For large t, the solutions satisfy Whitham's averaged equations at some times and the equations found by Flaschka et al. at other times.