Optical solitons to the generalized nonlinear Schrödinger equations for pulse propagation using several different techniques

Abstract

In this paper, we apply several different techniques, namely the extended auxiliary equation method, the new mapping method, the ϕ6- model expansion method, the Jacobi elliptic expansion method and the well-known solutions of Liénard equation for constructing many new exact solutions including Jacobi elliptic solutions to the generalized nonlinear Schrödinger equations for pulse propagation with negative index material embeded into a Kerr medium. This study confirms the accuracy and the efficiency of the used techniques. Comparing our new results with the well-known results are given. Comparing the obtained results yielding from the above several methods with each other are also obtained.