ON SOME NEW ANALYTICAL SOLUTIONS FOR THE (2+1)-DIMENSIONAL BURGERS EQUATION AND THE SPECIAL TYPE OF DODD-BULLOUGH-MIKHAILOV EQUATION

Abstract

Some new travelling wave transform methods are very important for obtaining analytical solutions of special type of nonlinear partial differential equations (NLPDEs). Some of these solutions of NLPDEs may be in the different forms such as rational function solutions, trigonometric function solutions, hyperbolic function solutions, exponential function solutions and Jacobi elliptic function solutions. These forms tell us the various properties of the NLPDEs from scientifical applications to engineering. In this research, we have studied to obtain the analytical solution of the nonlinear (2+1)-dimensional Burgers equation which is named from Johannes Martinus Burgers and the nonlinear special type of the Dodd-Bullough-Mikhailov equation introduced to the literature by Roger Dodd, Robin Bullough, and Alexander Mikhailov.