The N-soliton solutions for the matrix modified Korteweg–de Vries equation via the Riemann–Hilbert approach

Abstract

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.