Generalized Adler-Moser Polynomials and Multiple Vortex Rings for the Gross-Pitaevskii Equation
Generalized Adler-Moser Polynomials and Multiple Vortex Rings for the Gross-Pitaevskii Equation
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Gross-Pitaevskii 方程的广义 Adler-Moser 多项式和多重涡环
DOI：
10.1137/21m1394606
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发表时间：
2021
影响因子：
2
通讯作者：
Juncheng Wei
中科院分区：
文献类型：
--
作者：
Weiwei Ao;Yehui Huang;Yong Liu;Juncheng Wei
构造了三维Gross-Pitaevskii方程i t = t+（1-|Ψ| 2）R3 ×R上的复值函数。这些解具有2n + 1涡环的形状，彼此远离。在这些涡环中，n + 1个涡环具有正取向，另外n个涡环具有负取向。这些环的位置所描述的一个序列的多项式与合理的系数的根。这里发现的多项式可以被视为经典Adler-Moser多项式的推广，并且可以表示为某些非常特殊的函数的朗斯基。在这些多项式的推导中使用的技术应该有独立的兴趣。
New finite energy traveling wave solutions with small speed are constructed for the three dimensional Gross-Pitaevskii equation iΨt = ∆Ψ + (1− |Ψ|2)Ψ, where Ψ is a complex valued function defined on R3 ×R. These solutions have the shape of 2n + 1 vortex rings, far away from each other. Among these vortex rings, n + 1 of them have positive orientation and the other n of them have negative orientation. The location of these rings are described by the roots of a sequence of polynomials with rational coefficients. The polynomials found here can be regarded as a generalization of the classical AdlerMoser polynomials and can be expressed as the Wronskian of certain very special functions. The techniques used in the derivation of these polynomials should have independent interest.