Exact solutions and conservation laws of two-wave mode Kadomtsev-Petviashvili equation and a nonintegrable nonlinear equation

Abstract

In this dissertation we study three nonlinear partial differential equations namely the Korteweg-de Vries (KdV) equation as an illustrative example, nonintegrable nonlinear equation and two-wave mode Kadomtsev-Petviashvili (TKP) equation. We employ the multiplier method to find conservation laws. We also use Kudryashov and simplest equation methods to obtain exact solutions of a generalized two nonlinear partial differential equations.