Long-time asymptotics for the coupled complex short-pulse equation with decaying initial data

We characterize the long-time asymptotic behavior of the solution of the initial value problem for the coupled complex short -pulse equation associated with the 4 x 4 matrix spectral problem. The spectral analysis of the 4 x 4 matrix spectral problem is very difficult because of the existence of energy -dependent potentials and the WKI type. The method we adopted is a combination of the inverse scattering transform and Deift-Zhou nonlinear steepest descent method. Starting from the Lax pair associated with the coupled complex short -pulse equation, we derive a basic Riemann-Hilbert problem by introducing some appropriate spectral function transformations, and reconstruct the potential parameterized from the solution of the basic Riemann-Hilbert problem via the asymptotic behavior of the spectral variable at k -> 0. We finally obtain the leading order asymptotic behavior of the solution of the coupled complex short -pulse equation through a series of Deift-Zhou contour deformations. (c) 2023 Elsevier Inc. All rights reserved.