Applications of Lie Groups to Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1986
|
| Schriftenreihe: | Graduate Texts in Mathematics
107 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781468402742 9781468402766 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-0274-2 |
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Datensatz im Suchindex
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468402742 9781468402766 |
| issn | 0072-5285 |
| language | English |
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| spelling | Olver, Peter J. Verfasser aut Applications of Lie Groups to Differential Equations by Peter J. Olver New York, NY Springer US 1986 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 107 0072-5285 This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Differentialgleichung (DE-588)4012249-9 s Physik (DE-588)4045956-1 s 1\p DE-604 https://doi.org/10.1007/978-1-4684-0274-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Olver, Peter J. Applications of Lie Groups to Differential Equations Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Differentialgleichung (DE-588)4012249-9 gnd Physik (DE-588)4045956-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4045956-1 (DE-588)4035695-4 |
| title | Applications of Lie Groups to Differential Equations |
| title_auth | Applications of Lie Groups to Differential Equations |
| title_exact_search | Applications of Lie Groups to Differential Equations |
| title_full | Applications of Lie Groups to Differential Equations by Peter J. Olver |
| title_fullStr | Applications of Lie Groups to Differential Equations by Peter J. Olver |
| title_full_unstemmed | Applications of Lie Groups to Differential Equations by Peter J. Olver |
| title_short | Applications of Lie Groups to Differential Equations |
| title_sort | applications of lie groups to differential equations |
| topic | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Differentialgleichung (DE-588)4012249-9 gnd Physik (DE-588)4045956-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Differentialgleichung Physik Lie-Gruppe |
| url | https://doi.org/10.1007/978-1-4684-0274-2 |
| work_keys_str_mv | AT olverpeterj applicationsofliegroupstodifferentialequations |