Optical soliton solutions to the (2+1)-dimensional Kundu–Mukherjee–Naskar equation

Abstract

In this work, a new method has been applied for finding solutions to the Kundu–Mukherjee–Naskar (KMN) equation in (2[Formula: see text]+[Formula: see text]1) dimensions. These optical solutions were derived with the aid of a new method named the Exp-Function method. The method is used for solving the nonlinear governing equation, which contains high nonlinear term. This method is considered as an alternative technique for obtaining both analytical and approximate solutions for a different type of PDE with several applications in science and engineering. The efficiency of the proposed technique has been shown by a few test problems. By comparing the results obtained in this paper with other researchers it can be noticed that this method is a promising technique for finding solutions to other similar problems.

Dark soliton solutions to (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation via the first integral method

“…Using the above transformations, Eq. (2) is reduced to a nonlinear ordinary differential equation (NLODE) of the form 4where Next, let us put 5Then, we have a plane autonomous system (6) where H is a polynomial in R and S. If we can find two first integrals to this plane autonomous system under the same conditions, then analytic solutions of the system (6) can be obtained directly. However, in general, it is really difficult for us to realize this even for one first integral, because for a given plane autonomous system, there exists neither a systematic theory that can tell us how to find its first integrals nor a logical way for telling us what these first integrals are.…”

“…In the present decade, the study of the dynamics of optical soliton propagation through optical fibers yields many promising results in the research of optical communication systems. Several equations / models have been proposed so far in the past a few decades to describe such physical phenomena and the Kundu-Mukherjee-Naskar (KMN ) equation [1][2][3][4][5][6] is one of them. This equation was first proposed in the year 2014 by three Indian physicists namely Anjan Kundu, Abhik Mukherjee and Tapan Naskar for modelling the dynamics of two-dimensional rogue waves in ocean water and also two-dimensional ion-acoustic waves in magnetized plasmas [7,8].…”

Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

“…Rivzi et al [36] used csch method, extended Tanh-Coth method and extended rational sinh-cosh method to get the exact solutions of KMN model. Talarposhti et al [37] employed Exp-function method to yield the optical soliton solutions of considered KMN model.…”

Traveling wave solutions for the generalized (2+1)-dimensional Kundu-Mukherjee-Naskar equation

“…Subsequently, Kumar [22] discussed singular, dark, combined darksingular solitons and other hyperbolic solutions by using the csch method, extended tanh-coth method and extended rational sinh-cosh method. Meanwhile, Talarposhti [23] and Ghanbari [24] derived some new solitary solutions by using the Exp-function method. More recently, Rezazadeh constructed the analytical solutions of Eq.…”