Vector breather waves and higher-order rouge waves to the coupled higher-order nonlinear Schrödinger equations

ABSTRACT

We investigate the vector breather waves and higher-order rouge waves of the coupled higher-order nonlinear Schrödinger equations via the Darboux-dressing transformation. Firstly, based on the Darboux-dressing transformation, we introduce the asymptotic expansion theory, which allows the solution of the equation to be iterated through the same spectral parameters. Then, the matrix exponential function and the Taylor multi-series expansion method are used to derive the vector breather wave solutions and the higher-order rouge wave solutions. Moreover, we analyze the characteristic lines of the breather waves, which determine the dynamic behaviours of the breather waves. Finally, we give some conclusions of this work.

Keywords:

• The coupled higher-order nonlinear Schrödinger equations
• Darboux-dressing transformation
• breather waves
• rouge waves
• dynamic behaviours

2010 Mathematics Subject Classifications:

• 35Q51
• 35Q53
• 35C08

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We express our sincere thanks to the Editor and Reviewers for their valuable comments. This work was supported by the Fundamental Research Fund for the Central Universities under the Grant Nos. 2019ZDPY07.