The focusing coupled modified Korteweg–de Vries equation with nonzero boundary conditions: the Riemann–Hilbert problem and soliton classification

Xinxin Ma

Department of Mathematics, China University of Mining and Technology, Beijing, China

Abstract: The focusing coupled modified Korteweg–de Vries equation with nonzero boundary conditions is investigated by the Riemann–Hilbert approach. Three symmetries are formulated to derive compact exact solutions. The solutions include six different types of soliton solutions and breathers, such as dark–dark, bright–bright, kink–dark–dark, kink–bright–bright solitons, and a breather–breather solution.

Keywords: focusing coupled modified Korteweg–de Vries equation, nonzero boundary condition, dark–dark soliton, kink soliton, Riemann–Hilbert problem.

Received: 19.09.2023
Revised: 13.11.2023

DOI: 10.4213/tmf10615

 English version: Theoretical and Mathematical Physics, 2024, 219:1, 598–628

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