New Explicit Exact Solutions of Nonlinear Evolution Equations Using the Generalized Auxiliary Equation Method Combined with Exp-function Method

Abstract

In this paper, we utilize the Exp-function method with symbolic computational sys- tem Maple to constructing generalized solitary solutions of auxiliary equation. With the aid of auxiliary equation and its generalized solitary solutions, new exact solutions with three arbi- trary functions of two nonlinear evolution equations in physics, namely, higher-order nonlinear Schrodinger equation describing propagation of ultrashort pulses in nonlinear optical fibers and generalized Zakharov equations are obtained. It is shown that the Exp-function method provides a straightforward and important mathematical tool for nonlinear evolution equations arising in physics.