Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave equations

Abstract

Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and solves several drawbacks of some previous algorithms proposed in the literature. The method is illustrated with the numerical generation of periodic traveling waves of fractional KdV type equations and some extended Boussinesq systems.