Soliton Solutions for Nonlinear Systems (2+1)-Dimensional Equations

Abstract

This paper implemented two methods for solving Nonlinear systems of Partial differential equations. These are tanh method, and sine-cosine method. Methods have been successfully tested on Konopelchenko-Dubrovsky, and Dispersive Long Wave systems of equations. The calculations demonstrate the effectiveness and convenience of these two methods for solving nonlinear system of PDEs. Nonlinear evolution equations (NLEEs) have been the subject of study in various branches of Mathematical-physical sciences such as physics, biology, and chemistry. The analytical solutions of such equations are of fundamental importance since a lot of mathematical physical models are described by NLEEs. The nonlinear wave phenomena observed in the above mentioned scientific fields, are often modeled by the bell-shaped sech solutions and the kink-shaped tanh solutions. The availability of these exact solutions, for those nonlinear equations can greatly facilitate the verification of numerical solvers on the stability analysis of the solution. The investigation of exact solutions of NLPDEs plays an important role in the study of these phenomena. In the past several decades, many effective methods for obtaining exact solutions of NLPDEs have been presented. In the literature, there is a wide variety of approaches to nonlinear problems for constructing traveling wave solutions, such as Hirota's direct method (Hirota (2004)), tanh-sech method (Malfliet (1993),