Numerical Computation of Solitary Wave Solutions of the Rosenau Equation

TL;DR

This paper develops numerical methods using the Petviashvili iteration to compute solitary wave solutions of the Rosenau equation, demonstrating rapid convergence and robustness across various initial guesses.

Contribution

The paper introduces and applies Petviashvili-based numerical algorithms specifically tailored for the Rosenau equation with different nonlinearities.

Findings

Algorithms converge rapidly in numerical experiments.

Method is robust to various initial guesses.

Applicable to equations with different power law nonlinearities.

Abstract

We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then apply two numerical algorithms based on the Petviashvili method for solving the Rosenau equation with single or double power law nonlinearity. Numerical calculations rely on a uniform discretization of a finite computational domain. Through some numerical experiments we observe that the algorithm converges rapidly and it is robust to very general forms of the initial guess.