The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation

The inverse scattering transform is developed for a combined modified Korteweg de Vrie equation through the technique of Riemann Hilbert problems. From special Riemann Hilbert problems with an identity jump matrix, soliton solutions are generated, which corresponds to the inverse scattering problems with reflectionless coefficients. A specific example of two-soliton solutions is explicitly presented, together with its 3d plots, contour plots and x-curve plots. (C) 2018 Elsevier Inc. All rights reserved.