Bernoulli (G′/G)-expansion method for nonlinear Schrödinger equation with third-order dispersion

Abstract

In this paper, exact solutions of nonlinear Schrödinger equation with third-order dispersion in constant potential are achieved. This equation plays an important role in mathematical physics such as nonlinear optics. To deal with the mentioned equation, Bernoulli [Formula: see text]-expansion method has been proposed by exerting some transformation and using homogenous balance. On the other hand, [Formula: see text]-expansion method has also been used to obtain the addition results and find out the differences between the proposed method and the applied method. As a result of this study, the solutions of these two methods are expressed by hyperbolic function solutions and trigonometric function solutions. To have acceptable concept of dynamic structures of begotten results and find relation between these solutions and certain parameters, some figures are illustrated when the potential is taken as different values, which show us bright soliton and periodic wave. To complete our study, the Lagrangian and Hamiltonian of nonlinear Schrödinger equation with third-order dispersion are also established.