Bifurcations of Liouville tori in a system of two vortices of positive intensity in a Bose-Einstein condensate

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Abstract

In this paper we consider a completely Liouville integrable Hamiltonian system with two degrees of freedom, which describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a harmonic trap. For vortex pairs of positive intensity detected bifurcation of three Liouville tori into one. Such bifurcation was found in the integrable case of Goryachev-Chaplygin-Sretensky in the dynamics of a rigid body. For the integrable perturbation of the physical parameter of the intensity ratio, identified bifurcation proved to be unstable, which led to bifurcations of the type of two tori into one and vice versa.

About the authors

P. E. Ryabov

Finance University under the Government of the Russian Federation; Institute of Machines Sciense named after A.A. Blagonravov of the Russian Academy of Sciences; Udmurt State University

Author for correspondence.
Email: peryabov@fa.ru
Russian Federation, 49, Leningradsky avenue, Moscow, 125993; 4, Kcharitonievsky, Moscow, 101990; 1/1, Universitetskaya Street, Izhevsk, Udmurtia, 426034

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