On the N-tuple Wave Solutions of the Korteweg-de Vries Equation

Abstract

Each of such solutions is called a soliton or solitary wave solution. Recently it was discovered that there exist solutions of the KdV equation which behave like superposition of two solitons as t -> ± oo (Kruskal and Zabusky [JT]). The existence and properties of such solutions (called double wave solutions) were studied by Lax |Jf]. The structure of the solution of the KdV equation for the rapidly decreasing initial value was clarified by Gardner, Greene, Kruskal and Miura Q2]. They related the solution u(x, t) to the Schrodinger equation with the potential u (for each t) and found that discrete eigenvalues remain invariant. The reflection coefficient and the normalization coefficients

Locations

• Publications of the Research Institute for Mathematical Sciences - View - PDF