Green's Function Method for Periodic Traveling Wave Solutions of the KdV Equation

Abstract

Green's function method is used for studying periodic traveling wave solutions of a generalized KdV equation. It is shown through the construction of an explicit Green's function that the periodic boundary-value problem for the traveling wave solution of the KdV equation is equivalent to an integral equation with a symmetrical kernel which generates a compact operator in the space of periodic functions. This integral representation also leads to the existence of a periodic traveling wave solution for an associated inhomogeneous KdV equation.

Keywords:

• KdV equation,periodic traveling wave solution,Green's function,integral representation,

Additional information

Notes on contributors

Liu Bao-Ping

C. V. Pao

Ivar Stakgold