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Archive of Issues

Germany; Russia Jena; Yekaterinburg
Year
2016
Volume
26
Issue
2
Pages
245-257
 Section Mathematics Title Traveling waves in a profile of phase field: exact analytical solutions of a hyperbolic Allen-Cahn equation Author(-s) Nizovtseva I.G.a, Galenko P.K.b, Alexandrov D.V.a, Vikharev S.V.a, Titova E.A.a, Sukhachev I.S.a Affiliations Ural Federal Universitya, University of Jenab Abstract To obtain solutions of the hyperbolic Allen-Cahn equation, the first integral method, which follows from well-known Hilbert Null-theorem, is used. Exact analytical solutions are obtained in a form of traveling waves, which define complete class of the hyperbolic Allen-Cahn equation. It is shown that two subclasses of solutions exist within this complete class. The first subclass exhibits continual solutions and the second subclass is represented by solutions with singularity at the origin of coordinate system. Such non-uniqueness of solutions stands a question about stable attractor, i.e., about the traveling wave to which non-stationary solutions may attract. 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