Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction
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| Creator |
Anco, S.C.
Ali, S. Wolf, T. |
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| 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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| Date |
2019-02-13T18:41:43Z
2019-02-13T18:41:43Z 2011 |
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| Type |
Article
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| Identifier |
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/123456789/147188 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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