Resumen de On Behavior Analysis of Solutions for the Modified Complex Short Pulse Equation in the Space-Time Soliton Regions

Jia Wang, Xianguo Geng, Kedong Wang, Ruomeng Li

• The Riemann–Hilbert approach and ∂ steepest descent method are developed to study the soliton resolution conjecture for the modified complex short pulse equation with initial data in weighted Sobolev space. Based on the resulting Riemann–Hilbert problem, the long-time asymptotic expansion of the solution for the modified complex short pulse equation is derived in a fixed space-time cone. It is shown that the soliton resolution conjecture of the modified complex short pulse equation is composed of three parts: the leading term is an N(I)-soliton whose parameters are modulated by a set of localized soliton-soliton interactions as a soliton passes through the cone; the second t−1/2 order term arises from soliton-radiation interactions on the continuous spectrum; the third term is a residual error from a ∂-problem.