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
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.
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