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

TL;DR

This paper introduces a numerical method to generate periodic traveling wave solutions for nonlinear dispersive wave equations, improving upon previous algorithms by modifying a fixed point approach.

Contribution

It presents a novel modification of a fixed point algorithm that overcomes limitations of earlier methods for computing wave solutions.

Findings

Successfully generated solutions for fractional KdV equations

Extended Boussinesq systems solutions demonstrated

Method shows improved accuracy and stability

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.