ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmet...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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CTU Central Library
2016-06-01
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| Series: | Acta Polytechnica |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/3411 |
| _version_ | 1819017793205436416 |
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| author | Giorgio Gubbiotti Decio Levi Christian Scimiterna |
| author_facet | Giorgio Gubbiotti Decio Levi Christian Scimiterna |
| author_sort | Giorgio Gubbiotti |
| collection | DOAJ |
| description | In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries. |
| first_indexed | 2024-12-21T03:09:10Z |
| format | Article |
| id | doaj.art-90b058506d8a402cb3b0a55fa4ff674a |
| institution | Directory Open Access Journal |
| issn | 1210-2709 1805-2363 |
| language | English |
| last_indexed | 2024-12-21T03:09:10Z |
| publishDate | 2016-06-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-90b058506d8a402cb3b0a55fa4ff674a2022-12-21T19:18:01ZengCTU Central LibraryActa Polytechnica1210-27091805-23632016-06-0156319320110.14311/AP.2016.56.01933142ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONSGiorgio Gubbiotti0Decio Levi1Christian Scimiterna2Dept. Math. Phys. Roma Tre UniversityDip. Math. Phys. Roma Tre UniversityDept. Math. Phys. Roma Tre UniversityIn this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.https://ojs.cvut.cz/ojs/index.php/ap/article/view/3411Lie point symmetries, generalized symmetries, partial differential equations, partial difference equations, Darboux integrable systems, linearizable nonlinear equations |
| spellingShingle | Giorgio Gubbiotti Decio Levi Christian Scimiterna ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS Acta Polytechnica Lie point symmetries, generalized symmetries, partial differential equations, partial difference equations, Darboux integrable systems, linearizable nonlinear equations |
| title | ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS |
| title_full | ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS |
| title_fullStr | ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS |
| title_full_unstemmed | ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS |
| title_short | ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS |
| title_sort | on partial differential and difference equations with symmetries depending on arbitrary functions |
| topic | Lie point symmetries, generalized symmetries, partial differential equations, partial difference equations, Darboux integrable systems, linearizable nonlinear equations |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/3411 |
| work_keys_str_mv | AT giorgiogubbiotti onpartialdifferentialanddifferenceequationswithsymmetriesdependingonarbitraryfunctions AT deciolevi onpartialdifferentialanddifferenceequationswithsymmetriesdependingonarbitraryfunctions AT christianscimiterna onpartialdifferentialanddifferenceequationswithsymmetriesdependingonarbitraryfunctions |