Quasi-Lie schemes for PDEs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866909373931978752 |
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| author | Carinena, Jose F. Grabowski, Janusz de Lucas, Javier |
| author_facet | Carinena, Jose F. Grabowski, Janusz de Lucas, Javier |
| contents | The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of partial differential equations and its applications to obtaining $t$-dependent superposition rules and integrability conditions are analysed. We develop a procedure of constructing quasi-Lie systems through a generalisation to PDEs of the so-called theory of quasi-Lie schemes. Our techniques are illustrated with the analysis of Wess-Zumino-Novikov-Witten models, generalised Abel differential equations, Baecklund transformations, as well as other differential equations of physical and mathematical relevance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_02238 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Quasi-Lie schemes for PDEs Carinena, Jose F. Grabowski, Janusz de Lucas, Javier Analysis of PDEs Mathematical Physics Differential Geometry 34A26 (Primary), 34A05, 34A34, 17B66, 22E70 (Secondary) The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of partial differential equations and its applications to obtaining $t$-dependent superposition rules and integrability conditions are analysed. We develop a procedure of constructing quasi-Lie systems through a generalisation to PDEs of the so-called theory of quasi-Lie schemes. Our techniques are illustrated with the analysis of Wess-Zumino-Novikov-Witten models, generalised Abel differential equations, Baecklund transformations, as well as other differential equations of physical and mathematical relevance. |
| title | Quasi-Lie schemes for PDEs |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry 34A26 (Primary), 34A05, 34A34, 17B66, 22E70 (Secondary) |
| url | https://arxiv.org/abs/1712.02238 |