Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations
We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/181275 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849306673472077824 |
|---|---|
| author | Ivan Tsyfra Tomasz Czyżycki |
| author_facet | Ivan Tsyfra Tomasz Czyżycki |
| author_sort | Ivan Tsyfra |
| collection | DOAJ |
| description | We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional symmetry. Then we find solution to nonlinear heat equation which cannot be obtained in the framework of the classical Lie approach. By using operators of Lie-Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too. |
| format | Article |
| id | doaj-art-25e54b0fad4b4afca6b441f7f637124d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-25e54b0fad4b4afca6b441f7f637124d2025-08-20T03:55:00ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/181275181275Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type EquationsIvan Tsyfra0Tomasz Czyżycki1AGH University of Science and Technology, Faculty of Applied Mathematics, 30 Mickiewicza Avenue, 30-059 Krakow, PolandInstitute of Mathematics, University of Białystok, Ciołkowskiego 1M, 15-245 Białystok, PolandWe study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional symmetry. Then we find solution to nonlinear heat equation which cannot be obtained in the framework of the classical Lie approach. By using operators of Lie-Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too.http://dx.doi.org/10.1155/2015/181275 |
| spellingShingle | Ivan Tsyfra Tomasz Czyżycki Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations Abstract and Applied Analysis |
| title | Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations |
| title_full | Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations |
| title_fullStr | Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations |
| title_full_unstemmed | Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations |
| title_short | Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations |
| title_sort | nonpoint symmetry and reduction of nonlinear evolution and wave type equations |
| url | http://dx.doi.org/10.1155/2015/181275 |
| work_keys_str_mv | AT ivantsyfra nonpointsymmetryandreductionofnonlinearevolutionandwavetypeequations AT tomaszczyzycki nonpointsymmetryandreductionofnonlinearevolutionandwavetypeequations |