Generalized Adler-Moser Polynomials and Multiple vortex rings for the Gross-Pitaevskii equation
| Autor: | Ao, Weiwei, Huang, Yehui, Liu, Yong, Wei, Juncheng |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | New finite energy traveling wave solutions with small speed are constructed for the three dimensional Gross-Pitaevskii equation \begin{equation*} i\Psi_t= \Delta \Psi+(1-|\Psi|^2)\Psi, \end{equation*} where $\Psi$ is a complex valued function defined on ${\mathbb R}^3\times{\mathbb R}$. 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 Adler-Moser 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. Comment: 40 pages; comments are welcome |
| Databáze: | arXiv |
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