In this paper, we study the long-time asymptotic behavior of the solution of the Cauchy problem for the generalized Sasa-Satsuma equation. Starting with the 3 × 3 Lax pair related to the generalized Sasa-Satsuma equation, we construct a Rieman-Hilbert problem, by which the solution of the generalized Sasa-Satsuma equation is converted into the solution of the corresponding RiemanHilbert problem. Using the nonlinear steepest decent method for the Riemann-Hilbert problem, we obtain the leading-order asymptotics of the solution of the Cauchy problem for the generalized SasaSatsuma equation through several transformations of the Riemann-Hilbert problem and with the aid of the parabolic cylinder function.

中文翻译：

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广义Sasa-Satsuma方程的长时间渐近性

在本文中，我们研究了广义Sasa-Satsuma方程Cauchy问题解的长期渐近行为。从与广义Sasa-Satsuma方程有关的3×3 Lax对开始，构造一个Rieman-Hilbert问题，将广义Sasa-Satsuma方程的解转换为相应的RiemanHilbert问题的解。通过对Riemann-Hilbert问题使用非线性最陡体面方法，通过对Riemann-Hilbert问题的多次变换并借助抛物柱面函数，我们得到了广义SasaSatsuma方程Cauchy问题解的前向渐近性。