A study of equal-width and Zakharov-Kuznetsov-Burgers equations

Abstract

In this work we study some nonlinear partial differential equations which evolve in mathematical physics and other fields of science. We start by considering a second-order nonlinear Burgers equation as an illustration of what will be done in this dissertation. We then study the main equations of this dissertation. These equations are the equal-width equation and Zakharov-Kuznetsov-Burgers equations. 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.