Traveling waves in a profile of phase field: Exact analytical solutions of a hyperbolic Allen-Cahn equation / Nizovtseva I.G., Galenko P.K., Alexandrov D.V., Vikharev S.V., Titova E.A., Sukha-Chev I.S. // Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki. - 2016. - V. 26, l. 2. - P. 245-257.

ISSN:
19949197
Type:
Article
Abstract:
To obtain solutions of the hyperbolic Allen-Calm 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-Calm 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. The obtained solutions include earlier solutions for the parabolic Allen-Calm equation in a form of finite number of tanh-functions.
Author keywords:
Allen-Calm equation; Division theorem; First integral method; Traveling wave
Index keywords:
нет данных
DOI:
10.20537/vm160211
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Affiliations Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Ural Federal University, pr. Lenina, 51, Yekaterinburg, Russian Federation; Faculty of Physics and Astronomy, Friedrich Schiller University, Jena, Germany; Department of Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, pr. Lenina, 51, Yekaterinburg, Russian Federation; Laboratory of Combinatorial Algebra, Ural Federal University, pr. Lenina, 51, Yekaterinburg, Russian Federation
Author Keywords Allen-Calm equation; Division theorem; First integral method; Traveling wave
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Publisher Udmurt State University
Language of Original Document Russian
Abbreviated Source Title Vestn. Udmurt. Univ., Matematika, Mekhanika, Kompyuternye Nauki
Source Scopus