Conserved vectors and analytic solutions of potential Kadomtsev-Petviashvili and Korteweg-de Vries-like equations

Abstract

In this work, we study three nonlinear partial differential equations that are used to simulate a variety of physical processes in science. As an example of what will be done in this dissertation, we start off by looking at the second order nonlinear Boltzmann equation. The key equations that we examine in this dissertation are the potential Kadomtsev-Petviashvili and Kortewegde Vries-like equation. Lie symmetry analysis is employed to obtain commutation relations, one-parameter group of transformations and exact solution for the equations under study. Moreover, for more physical illustration of the extracted solutions, three and two dimensional plots for the solutions are presented. We further explore methods like Noether's approach, multiplier method and the conservation theorem due to Ibragimov to derive their conservation laws where they may apply.