Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations

In this work, we focus on a general procedure for finding exact travelling wave solutions for evolution equations with polynomial nonlinearites. Mathematically, looking for travelling wave solutions is asking the question whether a given PDE has solutions invariant under a Galilean transformation; in such a case, it can be reduced to an ODE. We discuss the existence of travelling wave solutions by using phase plane analysis. We show that popular methods such as the tanh-method, G0/G-method and many more are special cases of the presented approach. Analytical solutions to several examples of nonlinear equations are illustrated. In the application, we use the Maple program to compute solutions to nonlinear systems of equations.

Grantor dc:publisher

University of Pretoria

Year dc:date.issued

2022

Advisor dc:contributor.advisor

• Banasiak, Jacek

• UCTD
• Polynomial nonlinearites
• Travelling wave solutions
• Evolution equations
• Galilean transformation
• Tanh-method
• G0/G-method
• Maple program

Statement dc:rights

• © 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.

Language dc:language.iso

en

Dc Identifier Other

A2023

OAI identifier oai:identifier

oai:repository.up.ac.za:2263/88914