Long-Time Asymptotics for the Spin-1 Gross–Pitaevskii Equation
Long-Time Asymptotics for the Spin-1 Gross–Pitaevskii Equation
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DOI：
10.1007/s00220-021-03945-y
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发表时间：
2021-02
影响因子：
2.4
通讯作者：
X. Geng;Kedong Wang;Mingming Chen
中科院分区：
文献类型：
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作者：
X. Geng;Kedong Wang;Mingming Chen
在对与自旋1级Gross-Pitaevskii方程相关的Lax对和散射矩阵进行谱分析的基础上，将自旋1级Gross-Pitaevskii方程的柯西问题的解转化为相应的黎曼-希尔伯特问题的解。将Deift-Zhou非线性最速下降法推广到Riemann-Hilbert问题，通过Riemann-Hilbert问题跳跃矩阵的不同分解和矩阵值谱函数的分解，建立了Riemann-Hilbert问题模型。最后，得到了自旋1 Gross-Pitaevskii 方程柯西问题解的长时渐近性。
On the basis of the spectral analysis of theLax pair associated with the spin-1 Gross–Pitaevskii equation and the scattering matrix, the solution to the Cauchy problem of the spin-1 Gross–Pitaevskii equation is transformed into the solution to the corresponding Riemann–Hilbert problem. The Deift–Zhou nonlinear steepest descent method is extended to the Riemann–Hilbert problem, from which a model Riemann–Hilbert problem is established with the help of distinct factorizations of the jump matrix for the Riemann–Hilbert problem and a decomposition of the matrix-valued spectral function. Finally, the long-time asymptotics of the solution to the Cauchy problem of the spin-1 Gross–Pitaevskii equation is obtained.