Bifurcation Behaviour of the Travelling Wave Solutions of the Perturbed Nonlinear Schrödinger Equation with Kerr Law Nonlinearity

In the recent years, many direct methods have been developed to construct travelling wave solutions to the nonlinear partial differential equations (NLPDEs), such as the trigonometric function series method [1, 2], the modified mapping method and the extended mapping method [3], the modified trigonometric function series method [4], the dynamical system approach and the bifurcation method [5], the exp-function method [6], the multiple exp-function method [7], the transformed rational function method [8], the symmetry algebra method (consisting of Lie point symmetries) [9], the Wronskian technique [10], and so on. In addition they are efficient alternative methods for solving fractional differential equations, see [11 – 13]. In this paper, we investigate the perturbed NLSE with Kerr law nonlinearity [2]