(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2015)
In this article, the generalized expansion method has been successfully implemented to seek traveling wave solutions of the Eckaus equation and the nonlinear Schrödinger equation. The result reveals that the method together with the new ordinary differential equation is a very influential and effective tool for solving nonlinear partial differential equations in mathematical physics and engineering. The obtained solutions have been articulated by the hyperbolic functions, trigonometric functions and rational functions with arbitrary constants.