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Home » Issues » Archive of Issues » 2023 - 2 issue » pp. 240-258

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Russia Yaroslavl
Year
2023
Volume
33
Issue
2
Pages
240-258
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Section Mathematics
Title Stability and local bifurcations of single-mode equilibrium states of the Ginzburg-Landau variational equation
Author(-s) Kulikov D.A.a
Affiliations Yaroslavl State Universitya
Abstract One of the versions of the generalized variational Ginzburg-Landau equation is considered, supplemented by periodic boundary conditions. For such a boundary value problem, the question of existence, stability, and local bifurcations of single-mode equilibrium states is studied. It is shown that in the case of a nearly critical threefold zero eigenvalue, in the problem of stability of single-mode spatially inhomogeneous equilibrium states, subcritical bifurcations of two-dimensional invariant tori filled with spatially inhomogeneous equilibrium states are realized. The analysis of the stated problem is based on such methods of the theory of infinite-dimensional dynamical systems as the theory of invariant manifolds and the apparatus of normal forms. Asymptotic formulas are obtained for the solutions that form invariant tori.
Keywords Ginzburg-Landau variational equation, boundary value problem, stability, bifurcations, asymptotic formulas
UDC 517.977
MSC 37L10, 37L15
DOI 10.35634/vm230204
Received 11 January 2023
Language Russian
Citation Kulikov D.A. Stability and local bifurcations of single-mode equilibrium states of the Ginzburg-Landau variational equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 2, pp. 240-258.
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