Lie group analysis of the new extended KP and three-dimensional KP-BBM equations

Abstract

In this dissertation, we examine three partial deferential equations that are nonlin- ear. Namely, nonlinear filtration equation, the new extended Kadomtsev-Petviashvili equation (eKP) and the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation (KP-BBM). Nonlinear filtration equation is used as an illustrative example. The main equations of this dissertation are then examined. These equation's exact solutions are generated by Lie group analysis. The underlying equation's conservation laws are also determined using the multiplier method, Ibragimov's method and Noether theorem.