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Rational Solutions of Multi-component Nonlinear Schrödinger Equation and Complex Modified KdV Equation
  • Lihong Wang,
  • Jingsong He,
  • Róbert Erdélyi
Lihong Wang
Ningbo University

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Jingsong He
Shenzhen University
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Róbert Erdélyi
The University of Sheffield
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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.
21 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
21 Apr 2021Submission Checks Completed
21 Apr 2021Assigned to Editor
30 Apr 2021Reviewer(s) Assigned
28 Oct 2021Review(s) Completed, Editorial Evaluation Pending
29 Oct 2021Editorial Decision: Revise Minor
04 Nov 20211st Revision Received
04 Nov 2021Submission Checks Completed
04 Nov 2021Assigned to Editor
10 Nov 2021Reviewer(s) Assigned
12 Nov 2021Review(s) Completed, Editorial Evaluation Pending
22 Nov 2021Editorial Decision: Accept
Jun 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 9 on pages 5086-5110. 10.1002/mma.8094