Inverse scattering transform for the coupled modified complex short pulse equation: Riemann–Hilbert approach and soliton solutions

Abstract

In this paper, we develop a Riemann–Hilbert (RH) approach to the inverse scattering transform for the coupled modified complex short pulse (cmcSP) equation, which appeared as a reduction of the four-component system of short pulse type introduced by Popowicz in 2017. This approach allows us to present the general soliton solutions of the cmcSP equation in parametric form. Compared with the early results for the scalar modified complex short pulse equation, the cmcSP equation possesses richer soliton solutions, which include smooth solitons, cuspons, breathers and their various interactions.