Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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dc.contributor.author	Anco, S.C.
dc.contributor.author	Ali, S.
dc.contributor.author	Wolf, T.
dc.date.accessioned	2019-02-13T18:41:43Z
dc.date.available	2019-02-13T18:41:43Z
dc.date.issued	2011
dc.identifier.citation	Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction / S.C. Anco, S. Ali, T. Wolf // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 35K58; 35C06; 35A25; 58J70; 34C14
dc.identifier.other	DOI:10.3842/SIGMA.2011.066
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147188
dc.description.abstract	A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this group-foliation reduction method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. S. Anco and T. Wolf are each supported by an NSERC research grant. S. Ali thanks the Mathematics Department of Brock University for support during the period of a research visit when this paper was written. Computations were partly performed on computers of the Sharcnet consortium (www.sharcnet.ca). The referees and the editor are thanked for valuable comments which have improved this paper.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA