Work

Rational solutions of multi‐component nonlinear Schrödinger equation and complex modified KdV equation

Year: 2022

Type: article

Abstract: In this paper, the critical condition to achieve rational solutions of the multi-component nonlinear Schr\”odinger equation is proposed by introducing two nilpotent Lax matrices. Taking the series multisections of the vector eigenfunction as a set of fundamental eigenfunctions,an explicit formula of the $n$th-order rational solution is obtained by the degenerate Darboux transformation, which is used to generate some new patterns of rogue waves. A conjecture about the degree of the $n$th-order rogue waves is summarized. This conjecture also holds for rogue waves of the multi-component complex modified Korteweg-de Vries equation. Finally, the semi-rational solutions of the Manakov system are discussed.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.8094

Authors: Lihong Wang, Jingsong He, Róbert Erdélyi

Institutions: Ningbo University, University of Sheffield, Shenzhen University, Eötvös Loránd University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green