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

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. • A coupled modified complex short pulse (cmcSP) equation, whose spectral problem is of 4x4 matrix type, is considered. • A Riemann–Hilbert approach to the inverse scattering transform is developed for the cmcSP equation. • The general soliton solution formula of the cmcSP equation is obtained. • Rich solutions, such as smooth solitons, cuspons, breathers and their interactions, are presented for the cmsSP equation. [ABSTRACT FROM AUTHOR]