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Invariant varieties of the periodic boundary value problem of the nonlocal Ginzburg–Landau equation
Author(s) -
Kulikov Anatolii,
Kulikov Dmitrii
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7103
Subject(s) - mathematics , quasiperiodic function , attractor , boundary value problem , mathematical analysis , invariant (physics) , periodic boundary conditions , nonlinear system , initial value problem , mathematical physics , physics , quantum mechanics
One of the variants of the nonlocal Ginzburg–Landau equation is considered. This equation arises in the mathematical modeling of physical phenomena, such as ferromagnetism. For the corresponding initial boundary value problem in the case of periodic boundary conditions, current problems of the theory of infinite‐dimensional dynamical systems are considered. The question of the existence of smooth global solutions and a global attractor is studied. Its dimension and structure are determined. All the solutions of the nonlinear initial boundary value problem are found in explicit form. In particular, it was established that all the solutions belonging to the global attractor will be periodic or quasiperiodic functions of the temporal variable.