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 $t\to \infty$.

中文翻译：

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具有初始值问题的耦合色散AB系统解的长时间渐近性

在本文中，我们研究了耦合色散AB系统的基本Riemann-Hilbert（RH）问题，以及从Lax对开始的Schwartz类初值问题。我们使用Deift-Zhou非线性最速下降方法来分析所获得的RH问题，从而发现该耦合AB系统的解的长期渐近性为$Ť\to \infty$。