https://doi.org/10.1140/epjp/s13360-020-00575-6
Regular Article
The N-soliton solutions for the matrix modified Korteweg–de Vries equation via the Riemann–Hilbert approach
Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, People’s Republic of China
Received:
17
December
2019
Accepted:
29
June
2020
Published online:
15
July
2020
This paper focus on seeking the N-soliton solutions for the matrix mKdV equation, which generalizes to the multi-component mKdV equations and the coupled mKdV equations. By utilizing the technique of Riemann–Hilbert and investigating the spectral problem of the Lax pair, a class of Riemann–Hilbert problem will be discussed and established. Finally, in the case of irregularity and reflectionless, we derive the N-soliton solutions for a system of the matrix mKdV equation.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
