Study of a fifth order PDE using symmetries

TL;DR

This paper analyzes a family of fifth-order PDEs derived from an extended Lotka-Volterra system, focusing on symmetries and conservation laws to identify special cases of mathematical and biological interest.

Contribution

It performs symmetry and self-adjoint classifications on the PDE family, identifying new cases with conservation laws and justifying known special cases from literature.

Findings

Identification of special cases with non-trivial conservation laws

Justification of previously studied cases through symmetry analysis

Discovery of additional important cases for further research

Abstract

We study a family of PDEs, which was derived as an approximation of an extended Lotka-Volterra system, from the point of view of symmetries. Also, by performing the self adjoint classification on that family we offer special cases possessing non trivial conservation laws. Using both classifications we justify the particular cases studied in the literature, and we give additional cases that may be of importance.