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Generalized Kudryashov Method and General Exp a -Function Method for Solving a Higher Order Nonlinear Schrödinger Equation

Zayed EME and Al-Nowehy AG

In this article, two integration tools, namely the generalized Kudryashov method and the general Exp -function method, are applied to obtain many new exact solutions, symmetrical hyperbolic Fibonacci function solutions as well as bright, dark and singular soliton solutions of the nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity, selfsteeping and self-frequency shift effects which describes the propagation of an optical pulse in optical fibers. We compare the results yielding from these two methods. Also, a comparison between our results in this article and the well-known results are given.