New Soliton and Periodic Solutions for Two Nonlinear Physical Models

In the theoretical investigation, directly seeking exact solutions for nonlinear partial differential equations has become one of the central themes of perpetual interest in mathematical physics. Nonlinear wave phenomena appear in many fields, such as fluid mechanics, biomathematics, plasma physics, optical fibers, chemical physics, and other areas of engineering. These nonlinear phenomena are often related to nonlinear wave equations. In order to understand better these phenomena as well as to apply them in the practical life, it is important to seek their approximate solutions or more exact solutions. A variety of powerful methods have been developed for obtaining approximate and exact solutions for various nonlinear equations like the variational iteration method [1 – 3], F-expansion method [4, 5], tanh-function method [6 – 8], Adomian decomposition method [9, 10], homotopy perturbation method [11, 12], and so on. In this paper, we consider the Burgers-KadomtsevPetviashvili (Burgers-KP) equation in the following form [13]: