Inverse scattering and soliton solutions of high-order matrix nonlinear Schrödinger equation

The Riemann–Hilbert problem and soliton solutions to the high-order nonlinear Schrödinger equation with matrix version is studied with an equivalent spectral problem. Moreover, a pair of Jost solutions J^±, satisfied the asymptotic conditions J^±→ I and matrix spectral problem, can be used to obtain the matrix Riemann–Hilbert problem. This work makes the crucial use of the inverse scattering for the studied equation. In the case of reflection-less, based on the two type of zero structures of det (P⁺) , the different soliton solutions are theoretically and graphically presented.