Spectral Analysis and Long-Time Asymptotics of a Coupled Nonlinear Schrödinger System
Spectral Analysis and Long-Time Asymptotics of a Coupled Nonlinear Schrödinger System
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DOI：
10.1007/s40840-022-01354-5
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发表时间：
2022-07
影响因子：
1.2
通讯作者：
Kedong Wang;X. Geng;Mingming Chen;Ruomeng Li
中科院分区：
文献类型：
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作者：
Kedong Wang;X. Geng;Mingming Chen;Ruomeng Li
从一种新型耦合非线性Schr dinger系统的Lax对及其谱分析出发，构造了一个Riemann-Hilbert问题，并将该新型耦合非线性Schr dinger系统的Cauchy问题的解转化为Riemann-Hilbert问题的解.在基本Riemann-Hilbert问题的基础上，考虑Riemann-Hilbert问题轮廓的Deift-Zhou变形。借助Deift-Zhou非线性最速下降法，将基本Riemann-Hilbert问题转化为模型Riemann-Hilbert问题，并根据抛物柱面函数的渐近展开式，得到了模型Riemann-Hilbert问题解的首阶渐近性质.最后，我们得到了这类耦合非线性薛定谔方程组柯西问题解的长时间渐近性态。
Starting from theLax pair associated with a new type coupled nonlinear Schrödinger system and its spectral analysis, a Riemann–Hilbert problem is constructed, and the solution of Cauchy problem of the new type coupled nonlinear Schrödinger system is transformed into the solution of the Riemann–Hilbert problem. Based on the basic Riemann–Hilbert problem, the Deift–Zhou deformations to the contour of the Riemann–Hilbert problem are considered. With the aid of the Deift–Zhou nonlinear steepest descent method, the basic Riemann–Hilbert problem is transformed into a model Riemann–Hilbert problem and we derive the leading-order asymptotics of its solution according to the asymptotic expansions of the parabolic cylinder function. Finally, we obtain the long-time asymptotic behavior of solutions to the Cauchy problem of the new type coupled nonlinear Schrödinger system.