New bifurcation diagram in one model of vortex dynamics
- Authors: Palshin G.P.1
-
Affiliations:
- Финансовый университет при Правительстве Российской Федерации
- Issue: Vol 209 (2022)
- Pages: 33-41
- Section: Статьи
- URL: https://ogarev-online.ru/2782-4438/article/view/269872
- DOI: https://doi.org/10.36535/0233-6723-2022-209-33-41
- ID: 269872
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Abstract
We consider a completely Liouville-integrable Hamiltonian system with two degrees of freedom, which includes two limit cases. The first system describes the dynamics of two vortex filaments in a Bose–Einstein condensate enclosed in a harmonic trap. The second system governs the dynamics of point vortices in an ideal fluid in a circular domain. For the case of vortices with arbitrary intensities, we explicitly reduce the problem to a system with one degree of freedom. For intensities of different signs, we detect a new bifurcation diagram, which has not been previously encountered in works on this topic. Also, we obtain a separating curve, which is related to the change of the projections of Liouville tori without changing their number.
About the authors
G. P. Palshin
Финансовый университет при Правительстве Российской Федерации
Author for correspondence.
Email: gleb.palshin@yandex.ru
Russian Federation, Москва
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