Inverse Scattering Transform for the Coupled Modified Complex Short Pulse Equation: Multiple Higher Order Poles Case

ABSTRACT We develop a Riemann–Hilbert (RH) approach to the inverse scattering transform for the coupled modified complex short pulse (cmcSP) equation when the reflection coefficient has multiple higher order poles. With the help of a generalized cross product defined in four‐dimensional vector space, the discrete spectrum is specifically analyzed and the RH problem with generalized residue conditions at the pairs of higher order poles is constructed. In the reflectionless case, the RH problem can be reduced to a linear algebraic system. Consequently, the general formulas for the corresponding multiple higher order pole solutions of the cmcSP equation are obtained. The dynamical behavior of several pole‐type solutions is exhibited, including one double‐pole solutions (smooth solitons, cuspons, breathers), and several collisions between one double‐pole solution and one simple pole solution.