The hyperbolic Allen-Cahn equation: exact solutions / Nizovtseva I. G.,Galenko P. K.,Alexandrov D. V. // JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - 2016. - V. 49, l. 43.

ISSN/EISSN:

1751-8113 / 1751-8121

Type:

Article

Abstract:

Using the first integral method, a general set of analytical solutions is obtained for the hyperbolic Allen-Cahn equation. The solutions are presented by (i) the class of continual solutions described by tanh-profiles for traveling waves of the order parameter, and (ii) the class of singular solutions which exhibit unbounded discontinuity in the profile of the order parameter at the origin of the coordinate system. It is shown that the solutions include the previous analytical results for the parabolic Allen-Cahn equation as a limited class of tanh-functions, in which the inertial effects are omitted.

Author keywords:

exact solutions; Cahn-Allen; traveling wave; first integral method; division theorem TRAVELING-WAVE SOLUTIONS; NONLINEAR EVOLUTION-EQUATIONS; 1ST INTEGRAL METHOD; DE-VRIES EQUATION; INTERFACE; DYNAMICS; CRYSTAL; MOTION; MODELS

DOI:

10.1088/1751-8113/49/43/435201

Web of Science ID:

ISI:000385276300011

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	OCT 28
Publisher	IOP PUBLISHING LTD
Address	TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Language	English
Article-Number	435201
EISSN	1751-8121
Keywords-Plus	TRAVELING-WAVE SOLUTIONS; NONLINEAR EVOLUTION-EQUATIONS; 1ST INTEGRAL METHOD; DE-VRIES EQUATION; INTERFACE; DYNAMICS; CRYSTAL; MOTION; MODELS
Research-Areas	Physics
Web-of-Science-Categories	Physics, Multidisciplinary; Physics, Mathematical
Author-Email	nizovtseva.irina@gmail.com
ResearcherID-Numbers	Alexandrov, Dmitri/D-2516-2016
ORCID-Numbers	Alexandrov, Dmitri/0000-0002-6628-745X
Funding-Acknowledgement	Russian Science Foundation {[}16-11-10095]; Alexander von Humboldt Foundation {[}1160779]; German Research Foundation (DFG) {[}RE 1261/8-2]
Funding-Text	The authors acknowledge the support from the Russian Science Foundation (project no. 16-11-10095). I G N especially acknowledges the support of Alexander von Humboldt Foundation (ID 1160779). P K G especially acknowledges the support from German Research Foundation (DFG Project RE 1261/8-2).
Number-of-Cited-References	36
Usage-Count-Since-2013	1
Journal-ISO	J. Phys. A-Math. Theor.
Doc-Delivery-Number	DY6YR