Riemann-Hilbert problems and soliton solutions of nonlocal real reverse-spacetime mKdV equations

We would like to analyze a kind of nonlocal reverse-spacetime integrable PT-symmetric multicomponent modified Korteweg-de Vires (mKdV) equations by making a group of nonlocal reductions, and establish their associated Riemann-Hilbert problems which determine generalized Jost solutions of higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the associated Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. The Riemann-Hilbert problems in the reflectionless case are solved explicitly, and the resulting formulation of solutions enables us to present solitons to the nonlocal reverse-spacetime integrable PT-symmetric mKdV equations. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study analyzes a type of nonlocal reverse-spacetime integrable PT-symmetric mKdV equations by making nonlocal reductions and establishing associated Riemann-Hilbert problems. The solutions to Riemann-Hilbert problems in the reflectionless case enable the presentation of solitons to the equations.