Abundant solitary wave solutions to a perturbed Schrödinger equation with Kerr law nonlinearity via a novel approach

Abstract

The main purpose of the present paper is to introduce a reliable method, for the first time, in solving differential equations with partial derivatives. The significant idea behind this method is the modification of a well-known method. The main base functions used in the solution’s structures are Jacobi elliptic functions which are known functions and have many applications in practice. In order to achieve these results, the perturbed Schrödinger equation with Kerr law nonlinearity is considered. This nonlinear equation illustrates the propagation of optical solitons in nonlinear optical fibers. Thereupon, several analytical solutions corresponding to this model are obtained through employing an improved generalized exponential rational function method. Then we present a new version of it that is presented for the first time in the literature. Using these methods, several wave solutions related to the considered model are obtained. Moreover, several numerical simulations relevant to the resulting solutions are performed in the paper. As a notable features of the proposed method, the obtained solutions are characterized by the Jacobi elliptic functions. These solutions contain an index that for some specific choices is reduced to standard functions such as trigonometric and hyperbolic. The obtained results and solutions can be used for investigating the mechanism of several nonlinear phenomena laboratory and space plasmas. All necessary calculations are performed via symbolic packages of Wolfram Mathematica.

Keywords

• Analytical methods
• Jacobi elliptic functions
• Symbolic structures
• The perturbed Schrödinger equation