Abstract Starting from a specific example of 4 × 4 matrix spectral problems, an integrable coupled hierarchy, which includes a three-component coupled nonlinear Schrodinger system as the first nonlinear one, is generated, and an associated oscillatory Riemann–Hilbert problem is formulated. With the nonlinear steepest descent method, the leading long-time asymptotics for the Cauchy problem of the three-component coupled nonlinear Schrodinger system is computed, through deforming the oscillatory Riemann–Hilbert problem into a model one which is solvable.

中文翻译：

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三分量耦合非线性薛定谔系统的长时间渐近

摘要 从 4 × 4 矩阵谱问题的一个具体例子出发，生成了一个可积耦合层次结构，其中包括一个三分量耦合非线性薛定谔系统作为第一个非线性系统，并制定了一个相关的振荡 Riemann-Hilbert 问题。使用非线性最速下降法，通过将振荡黎曼-希尔伯特问题变形为可解模型，计算了三分量耦合非线性薛定谔系统柯西问题的领先长时间渐近线。