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

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...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2011
Автори: Anco, S.C., Ali, S., Wolf, T.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2011
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/147187
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Anco, S.C.
Ali, S.
Wolf, T.
author_facet Anco, S.C.
Ali, S.
Wolf, T.
citation_txt 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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
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spelling Anco, S.C.
Ali, S.
Wolf, T.
2019-02-13T18:41:09Z
2019-02-13T18:41:09Z
2011
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.
1815-0659
2010 Mathematics Subject Classification: 35K58; 35C06; 35A25; 58J70; 34C14
DOI:10.3842/SIGMA.2011.066
https://nasplib.isofts.kiev.ua/handle/123456789/147187
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.
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.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
Article
published earlier
spellingShingle Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
Anco, S.C.
Ali, S.
Wolf, T.
title Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
title_full Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
title_fullStr Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
title_full_unstemmed Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
title_short Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
title_sort exact solutions of nonlinear partial differential equations by the method of group foliation reduction
url https://nasplib.isofts.kiev.ua/handle/123456789/147187
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