The Deift–Zhou steepest descent method to long-time asymptotics for the Sasa–Satsuma equation
The Deift–Zhou steepest descent method to long-time asymptotics for the Sasa–Satsuma equation
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DOI：
10.1016/j.jde.2018.07.026
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发表时间：
2018-12
影响因子：
2.4
通讯作者：
Huan Liu;X. Geng;Bo Xue
中科院分区：
文献类型：
--
作者：
Huan Liu;X. Geng;Bo Xue
Sasa–Satsuma 方程的初值问题在相应的 Lax 对的帮助下转化为 3×3 矩阵 Riemann–Hilbert 问题。给出了跳跃矩阵的两种不同的因式分解和向量值函数ρ(k)的分解，利用非线性最速下降法得到了具有衰减初始数据的Sasa-Satsuma方程的长时间渐近性。
The initial value problem for the Sasa–Satsuma equation is transformed to a 3× 3 matrix Riemann–Hilbert problem with the help of the corresponding Lax pair. Two distinct factorizations of the jump matrix and a decomposition of the vector-valued function ρ (k) are given, from which the long-time asymptotics for the Sasa–Satsuma equation with decaying initial data is obtained by using the nonlinear steepest descent method.