Higher dimensional localized and periodic wave dynamics in an integrable (2+1)-dimensional deep water oceanic wave 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 and stability of the considered model is also investigated. 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.

Keywords:

• (2+1)-dimensional nonlinear model
• Kundu–Mukherjee–Naskar equation
• Jacobian-elliptic solution
• bright/dark soliton
• rational solution
• complexiton

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

One of the authors Sudhir Singh would like to thank Ministry of Human Resource Development, Govt. of India, and National Institute of Technology, Tiruchirappalli, India, for financial support through Institute Fellowship. Abhik Mukherjee acknowledges the Ministry of Science and Higher Education of the Russian Federation for partial financial support in the framework of Increase Competitiveness Program of NUST MISiS (K4-2018-061), implemented by a governmental decree dated 16 th of March 2013, N211. K. Sakkaravarthi was supported by Department of Science and Technology -- Science and Engineering Research Board (DST-SERB), Govt. of India, sponsored National Post-Doctoral Fellowship (File No. PDF/2016/000547).