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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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Інститут математики НАН України
2011
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147187 |
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irk-123456789-1471872019-02-14T01:26:02Z Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction Anco, S.C. Ali, S. Wolf, T. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147187 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| 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. |
| format |
Article |
| author |
Anco, S.C. Ali, S. Wolf, T. |
| spellingShingle |
Anco, S.C. Ali, S. Wolf, T. Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Anco, S.C. Ali, S. Wolf, T. |
| author_sort |
Anco, S.C. |
| title |
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_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_sort |
exact solutions of nonlinear partial differential equations by the method of group foliation reduction |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147187 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ancosc exactsolutionsofnonlinearpartialdifferentialequationsbythemethodofgroupfoliationreduction AT alis exactsolutionsofnonlinearpartialdifferentialequationsbythemethodofgroupfoliationreduction AT wolft exactsolutionsofnonlinearpartialdifferentialequationsbythemethodofgroupfoliationreduction |
| first_indexed |
2023-05-20T17:26:49Z |
| last_indexed |
2023-05-20T17:26:49Z |
| _version_ |
1796153313617510400 |