Generalized Adler--Moser Polynomials and Multiple Vortex Rings for the Gross--Pitaevskii Equation
Year: 2021
Type: article
Abstract: New finite energy traveling wave solutions with small speed are constructed for the three dimensional Gross--Pitaevskii equation. 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.
DOI: 10.1137/21m1394606
Authors: Weiwei Ao, Yehui Huang, Yong Liu, Juncheng Wei
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3121215195