Auto-B???cklund Transformation for Travelling Wave Solutions of Some Nonlinear Partial Differential Equations

Abstract

In this paper, we implemented Auto-B???cklund transformation for finding the travelling wave solutions ofthe complexly coupled KdV equations and the sixth order equation of the Burgers hierarchy. Thesesolutions are hyperbolic function solutions and exponential function solutions. It was observed using theMathematica program that these solutions provided the nonlinear partial differential equation and thenonlinear partial differential equation pair. Then, the solutions of these equations are compared with thesolutions of the same equations obtained in the literature using other methods. As a result of thecomparison, it was seen that some solutions are the same and some solutions are similar. The AutoB???cklund transformation used in this article is a powerful method for finding traveling wave solutions ofnonlinear partial differential equations.