Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations
We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal symmetries and formulae of nonlocal nonlinear superposition...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147789 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations / V. Tychynin, O. Petrova, O. Tertyshnyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 40 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147789 |
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Tychynin, V. Petrova, O. Tertyshnyk, O. 2019-02-16T08:11:35Z 2019-02-16T08:11:35Z 2007 Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations / V. Tychynin, O. Petrova, O. Tertyshnyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 40 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35A30; 35K55; 35K57; 35L70 https://nasplib.isofts.kiev.ua/handle/123456789/147789 We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal symmetries and formulae of nonlocal nonlinear superposition of solutions of these equations were used then for construction of chains of exact solutions. Linearization by means of the Legendre transformations of a second-order PDE with three independent variables allowed to obtain nonlocal superposition formulae for solutions of this equation, and to generate new solutions from group invariant solutions of a linear equation. The authors would like to thank the referees for helpful suggestions and comment. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations |
| spellingShingle |
Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations Tychynin, V. Petrova, O. Tertyshnyk, O. |
| title_short |
Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations |
| title_full |
Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations |
| title_fullStr |
Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations |
| title_full_unstemmed |
Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations |
| title_sort |
nonlocal symmetries and generation of solutions for partial differential equations |
| author |
Tychynin, V. Petrova, O. Tertyshnyk, O. |
| author_facet |
Tychynin, V. Petrova, O. Tertyshnyk, O. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal symmetries and formulae of nonlocal nonlinear superposition of solutions of these equations were used then for construction of chains of exact solutions. Linearization by means of the Legendre transformations of a second-order PDE with three independent variables allowed to obtain nonlocal superposition formulae for solutions of this equation, and to generate new solutions from group invariant solutions of a linear equation.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147789 |
| citation_txt |
Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations / V. Tychynin, O. Petrova, O. Tertyshnyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 40 назв. — англ. |
| work_keys_str_mv |
AT tychyninv nonlocalsymmetriesandgenerationofsolutionsforpartialdifferentialequations AT petrovao nonlocalsymmetriesandgenerationofsolutionsforpartialdifferentialequations AT tertyshnyko nonlocalsymmetriesandgenerationofsolutionsforpartialdifferentialequations |
| first_indexed |
2025-12-07T16:42:24Z |
| last_indexed |
2025-12-07T16:42:24Z |
| _version_ |
1850868492454068224 |