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Dynamics of Three Vortices in a Two-Layer Rotating Fluid

Abstract : The problem of studying the motion of three vortex lines with arbitrary intensities in an unbounded two-dimensional finite-thickness layer of a homogeneous fluid is known to belong to the class of integrable problems. However, a complete classification of possible motions was constructed only recently, see e. g. [J. Tavantzis and L. Ting, Phys. Fluids 31, No. 6, 1392–1409 (1988; Zbl 0657.76026)]. In [the authors, Regul. Chaotic Dyn. 7, No. 4, 435–472 (2002; Zbl 1020.76011)], a generalization is given for two-layer rotating fluid in the particular case determined by the conditions of (i) zero total circulation of vortices, and (ii) the equality of the intensities of two vortices. Here, the first of these restrictions is lifted.
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Mikhail Sokolovskiy, Jacques Verron. Dynamics of Three Vortices in a Two-Layer Rotating Fluid. Regular and Chaotic Dynamics, MAIK Nauka/Interperiodica, 2004, 9 (4), pp.417-438. ⟨10.1070/RD2004v009n04ABEH000288⟩. ⟨hal-00230193⟩

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