Long-time asymptotics of solutions for the coupled dispersive AB system with initial value problems

Abstract

In this paper, we study the basic Riemann-Hilbert (RH) problem of the coupled dispersive AB system with the Schwartz class of initial value problems starting from the Lax pair. We use the Deift-Zhou nonlinear steepest-descent method to analyze the obtained RH problem such that the long-time asymptotics of the solutions of this coupled AB system is found as t→∞.