Higher dimensional localized and periodic wave dynamics in a new integrable (2+1)-dimensional Kundu-Mukherjee-Naskar model

Abstract

In this article, a new integrable (2+1)-dimensional Kundu-Mukherjee-Naskar model which is a variant of the well known nonlinear Schrödinger equation is investigated. Bright-dark optical solitons along with periodic waves, complexiton and rational solutions are constructed by employing a generalized traveling wave analysis, Jacobian-elliptic function, Riccati equation and ansatz approach. Further, the dynamics of these bright/dark optical solitons and complexiton/periodic waves are studied by exploring the importance of arbitrary physical parameters with graphical demonstrations for a clear understanding. The obtained higher dimensional nonlinear wave solutions of this integrable system shall have useful applications in different physical systems including the dynamics of beam propagation in optical fibers, ion-acoustic waves in magnetized plasma and deep water oceanic rogue waves.

Integrability via Functional Expansion for the KMN Model

“…The general solution of ( 14) can be expressed in terms of elliptic functions [30]. Despite this direct solving possibility, here we will consider another approach.…”