A study of a generalized potential Yu-Toda-Sasa- Fukuyama and fifth-order nonlinear partial differential equations

Abstract

In this work we study two nonlinear partial differential equations which arise in mathematical physics. These equations have been studied in the literature. However, we start by considering a second-order nonlinear Benjamin-Bona-Mahony equation as an illustrative example. We then focus on the (3+1)-dimensional generalized potential Yu-Toda-Sasa-Fukuyama equation and the generalized fifth-order Korteweg-de Vries equation. Lie group analysis is used to construct exact solutions of these equations. Furthermore, conservation laws are derived for the underlying equations using the multiplier method and Noether's method.