Application of a Variation Expansion Method to the Nonlinear Sixth Order Ramani Equation

Abstract

Exact traveling wave solutions of the nonlinear sixth-order Ramani equation are obtained in this paper by means of a variant of the -expansion method. The variant pairs the usual auxiliary function with a Riccati-type function F, which turns the problem into a system of algebraic equations that is solved symbolically. Three sets of parameter values are found, and the resulting solutions are expressed through the hyperbolic function's tanh and coth. Every solution has been verified by direct substitution into the reduced ordinary differential equation.