Geodesic
New bifurcation diagram in one model of vortex dynamics
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 33-41

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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.
Keywords: vortex dynamics, completely integrable Hamiltonian system, bifurcation diagram, integral mapping, Bose–Einstein condensate.
Mots-clés : bifurcations of Liouville tori 
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     author = {G. P. Palshin},
     title = {New bifurcation diagram in one model of vortex dynamics},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {33--41},
     publisher = {mathdoc},
     volume = {209},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_209_a3/}
}
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G. P. Palshin. New bifurcation diagram in one model of vortex dynamics. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 33-41. http://geodesic.mathdoc.fr/item/INTO_2022_209_a3/