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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-02-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/019/ |
| _version_ | 1811192279971397632 |
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| author | Valentyn Tychynin Olga Petrova Olesya Tertyshnyk |
| author_facet | Valentyn Tychynin Olga Petrova Olesya Tertyshnyk |
| author_sort | Valentyn Tychynin |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T23:49:57Z |
| format | Article |
| id | doaj.art-9477779fc16341cb9cd674280a63437a |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-11T23:49:57Z |
| publishDate | 2007-02-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-9477779fc16341cb9cd674280a63437a2022-12-22T03:56:32ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-02-013019Nonlocal Symmetries and Generation of Solutions for Partial Differential EquationsValentyn TychyninOlga PetrovaOlesya TertyshnykWe 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.http://www.emis.de/journals/SIGMA/2007/019/Lie classical symmetrynonlocal symmetriesformulae for generation of solutionsnonlinear superposition principle |
| spellingShingle | Valentyn Tychynin Olga Petrova Olesya Tertyshnyk Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations Symmetry, Integrability and Geometry: Methods and Applications Lie classical symmetry nonlocal symmetries formulae for generation of solutions nonlinear superposition principle |
| title | 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_short | Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations |
| title_sort | nonlocal symmetries and generation of solutions for partial differential equations |
| topic | Lie classical symmetry nonlocal symmetries formulae for generation of solutions nonlinear superposition principle |
| url | http://www.emis.de/journals/SIGMA/2007/019/ |
| work_keys_str_mv | AT valentyntychynin nonlocalsymmetriesandgenerationofsolutionsforpartialdifferentialequations AT olgapetrova nonlocalsymmetriesandgenerationofsolutionsforpartialdifferentialequations AT olesyatertyshnyk nonlocalsymmetriesandgenerationofsolutionsforpartialdifferentialequations |