Lie-Bäcklund transformations in applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)
1979
|
| Series: | SIAM studies in applied mathematics
1 |
| Subjects: | |
| Online Access: | TUM01 UBW01 UBY01 UER01 Volltext |
| Item Description: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (p. 119-121) and index Introduction -- Classical foundations -- Surface-transformations: Lie's first questions; Finite-order generalization; Infinite-order structure -- Tranformation of families of surfaces: Lie's second question; Bianchi-Lie tranformation; Backlund transformations -- Examples of Backlund transformations: Invariance transformations -- Transformations relating different differential equations -- Tangent transformation groups: Finite-order tangent tranformations; Tangent transformation groups of Sophus Lie; Higher-order tangent transformation groups; Infinite-order tangent transformations -- Lie-Backlund tangent transformation groups; Lie-Backlund equations -- Application to differential equations: Defining equations -- Group theoretical nature of conservation laws; Lie via Lie-Backlund for ordinary differential equations; Group theoretical equivalence of quantum-mechanical systems -- Some applications of Backlund transformations: Nonlinear optics; Solitons and the KdV equation; Constants of the motion and conservation laws; Weakly dispersive shallow-water waves in two space dimensions This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity |
| Physical Description: | 1 Online Resource (x, 124 Seiten) |
| ISBN: | 9780898711516 |
| DOI: | 10.1137/1.9781611970913 |
Staff View
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| indexdate | 2024-07-10T00:10:18Z |
| institution | BVB |
| isbn | 9780898711516 |
| language | English |
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| publishDate | 1979 |
| publishDateSearch | 1979 |
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| series2 | SIAM studies in applied mathematics |
| spelling | Anderson, Robert Leonard 1933- Verfasser (DE-588)108926982X aut Lie-Bäcklund transformations in applications Robert L. Anderson, Nail H. Ibragimov Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) 1979 1 Online Resource (x, 124 Seiten) txt rdacontent c rdamedia cr rdacarrier SIAM studies in applied mathematics 1 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references (p. 119-121) and index Introduction -- Classical foundations -- Surface-transformations: Lie's first questions; Finite-order generalization; Infinite-order structure -- Tranformation of families of surfaces: Lie's second question; Bianchi-Lie tranformation; Backlund transformations -- Examples of Backlund transformations: Invariance transformations -- Transformations relating different differential equations -- Tangent transformation groups: Finite-order tangent tranformations; Tangent transformation groups of Sophus Lie; Higher-order tangent transformation groups; Infinite-order tangent transformations -- Lie-Backlund tangent transformation groups; Lie-Backlund equations -- Application to differential equations: Defining equations -- Group theoretical nature of conservation laws; Lie via Lie-Backlund for ordinary differential equations; Group theoretical equivalence of quantum-mechanical systems -- Some applications of Backlund transformations: Nonlinear optics; Solitons and the KdV equation; Constants of the motion and conservation laws; Weakly dispersive shallow-water waves in two space dimensions This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity Differential equations Bäcklund transformations Transformation groups Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf Lie-Bäcklund-Transformation (DE-588)4297640-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Lie-Bäcklund-Transformation (DE-588)4297640-6 s 1\p DE-604 Transformation Mathematik (DE-588)4060637-5 s 2\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 3\p DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s 4\p DE-604 Ibragimov, Nailʹ Ch. 1939- Sonstige (DE-588)172164419 oth Erscheint auch als Druckausgabe 9780898711516 SIAM studies in applied mathematics 1 (DE-604)BV047229985 1 https://doi.org/10.1137/1.9781611970913 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anderson, Robert Leonard 1933- Lie-Bäcklund transformations in applications SIAM studies in applied mathematics Differential equations Bäcklund transformations Transformation groups Numerische Mathematik (DE-588)4042805-9 gnd Transformation Mathematik (DE-588)4060637-5 gnd Lie-Bäcklund-Transformation (DE-588)4297640-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4060637-5 (DE-588)4297640-6 (DE-588)4044779-0 |
| title | Lie-Bäcklund transformations in applications |
| title_auth | Lie-Bäcklund transformations in applications |
| title_exact_search | Lie-Bäcklund transformations in applications |
| title_full | Lie-Bäcklund transformations in applications Robert L. Anderson, Nail H. Ibragimov |
| title_fullStr | Lie-Bäcklund transformations in applications Robert L. Anderson, Nail H. Ibragimov |
| title_full_unstemmed | Lie-Bäcklund transformations in applications Robert L. Anderson, Nail H. Ibragimov |
| title_short | Lie-Bäcklund transformations in applications |
| title_sort | lie backlund transformations in applications |
| topic | Differential equations Bäcklund transformations Transformation groups Numerische Mathematik (DE-588)4042805-9 gnd Transformation Mathematik (DE-588)4060637-5 gnd Lie-Bäcklund-Transformation (DE-588)4297640-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations Bäcklund transformations Transformation groups Numerische Mathematik Transformation Mathematik Lie-Bäcklund-Transformation Partielle Differentialgleichung |
| url | https://doi.org/10.1137/1.9781611970913 |
| volume_link | (DE-604)BV047229985 |
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