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2017•Proceedings of the American Mathematical SocietyRequires access

Characteristics of the breather and rogue waves in a (2+1)-dimensional nonlinear Schrödinger equation

Xiu‐Bin Wang, Shou‐Fu Tian, Tian‐Tian Zhang

Open publisher page 125 citations

Abstract

Under investigation in this paper is a (2+1)-dimensional nonlinear Schrödinger equation (NLS), which is a generalisation of the NLS equation. By virtue of Wronskian determinants, an effective method is presented to succinctly construct the breather wave and rogue wave solutions of the equation. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that rogue waves can come from the extreme behavior of the breather waves. It is hoped that our results could be useful for enriching and explaining some related nonlinear phenomena.

About this research paper

What this paper is about

Under investigation in this paper is a (2+1)-dimensional nonlinear Schrödinger equation (NLS), which is a generalisation of the NLS equation. By virtue of Wronskian determinants, an effective method is presented to succinctly construct the breather wave and rogue wave solutions of the equation. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that rogue waves can come from the extreme behavior of the breather waves. It is hoped that our results could be useful for enriching and explaining some related nonlinear phenomena.

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OpenAlex reports 125 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Method / approach

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Available abstract

Under investigation in this paper is a (2+1)-dimensional nonlinear Schrödinger equation (NLS), which is a generalisation of the NLS equation. By virtue of Wronskian determinants, an effective method is presented to succinctly construct the breather wave and rogue wave solutions of the equation. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that rogue waves can come from the extreme behavior of the breather waves. It is hoped that our results could be useful for enriching and explaining some related nonlinear phenomena.

Key concepts: Breather, Rogue wave, Wronskian, Nonlinear Schrödinger equation, Nonlinear system, Physics, Classical mechanics, Mathematical analysis

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