A two-component modified Korteweg–de Vries equation: Riemann–Hilbert problem and multi-soliton solutions

Abstract

In this paper, the inverse scattering transform of a two-component modified Korteweg–de Vries equation is under investigation, which is one of the important nonlinear models in mathematics and physics. The spectral analysis with a $4\times 4$ Lax pair is performed for the two-component modified Korteweg–de Vries equation, from which a Riemann Hilbert problem is strictly formulated. Moreover, multi-soliton solutions to the two-component modified Korteweg–de Vries equation are obtained through a particular Riemann–Hilbert formulation. Finally, some figures are presented to reveal the soliton features of the two-component modified Korteweg–de Vries equation.

Keywords:

• Two-component modified Korteweg–de Vries equation
• inverse scattering transform
• Riemann–Hilbert problem
• multi-soliton solutions
• Lax pairs

2010 Mathematics Subject Classifications:

• PACS 35Q51
• 35Q53
• 35C99
• 68W30
• 74J35

Acknowledgments

We express our sincere thanks to the Editor and Reviewers for their valuable comments.

Disclosure statement

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