Exact Solutions for a Class of Nonlinear PDE with Variable Coefficients Using ET and ETEM

Abstract

In this article, by using the modified CK direct method, we give a relationship between the generalized fifth-order KDV equations with variable coefficients and the corresponding constant coefficients ones. Then, we construct the abundant travelling solutions by the extended trial equation method (ETEM) in terms of different functions, such as the elliptic functions, rational functions, hyperbolic functions and trigonometric functions. The extended trial equation method is powerful and can be used to other partial differential equations and more research can be done by this method.

Wave Solutions for a (2 + 1)-Dimensional Burgers–KdV Equation with Variable Coefficients via the Functional Expansion Method

“…For the equation with variable coefficients, this task requires special care. It has been shown that, in some cases, it is possible to associate to each such equation an equation with constant coefficients [37]. To find solutions to the latter equation, the most convenient approach is to reduce the considered NPDE to a nonlinear ordinary differential equation (NODE).…”