Contact geometry and non-linear differential equations /:
Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibil...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2007.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
volume 101. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology). |
| Beschreibung: | 1 online resource (xxi, 496 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 487-492) and index. |
| ISBN: | 9781461941484 1461941482 9780511735141 0511735146 1139883089 9781139883085 0511889755 9780511889752 1107383935 9781107383937 1107387442 9781107387447 1107390362 9781107390362 1107398770 9781107398771 |
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| 588 | 0 | |a Print version record. | |
| 520 | |a Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology). | ||
| 546 | |a English. | ||
| 650 | 0 | |a Contact manifolds. |0 http://id.loc.gov/authorities/subjects/sh85031507 | |
| 650 | 0 | |a Differential equations, Nonlinear. |0 http://id.loc.gov/authorities/subjects/sh85037906 | |
| 650 | 6 | |a Variétés de contact (Géométrie) | |
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| _version_ | 1816882243958734848 |
| adam_text | |
| any_adam_object | |
| author | Kushner, Alexei |
| author2 | Lychagin, V. V. (Valentin Vasilʹevich) Rubtsov, Vladimir, 1952- |
| author2_role | |
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| author_GND | http://id.loc.gov/authorities/names/no2007033467 http://id.loc.gov/authorities/names/n85180906 http://id.loc.gov/authorities/names/no2007032818 |
| author_facet | Kushner, Alexei Lychagin, V. V. (Valentin Vasilʹevich) Rubtsov, Vladimir, 1952- |
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| contents | Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds. |
| ctrlnum | (OCoLC)857769650 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn857769650 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:31Z |
| institution | BVB |
| isbn | 9781461941484 1461941482 9780511735141 0511735146 1139883089 9781139883085 0511889755 9780511889752 1107383935 9781107383937 1107387442 9781107387447 1107390362 9781107390362 1107398770 9781107398771 |
| language | English |
| oclc_num | 857769650 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxi, 496 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Kushner, Alexei. http://id.loc.gov/authorities/names/no2007033467 Contact geometry and non-linear differential equations / Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov. Contact geometry and nonlinear differential equations Cambridge, UK ; New York : Cambridge University Press, 2007. 1 online resource (xxi, 496 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; volume 101 Includes bibliographical references (pages 487-492) and index. Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds. Print version record. Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology). English. Contact manifolds. http://id.loc.gov/authorities/subjects/sh85031507 Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Variétés de contact (Géométrie) Équations différentielles non linéaires. MATHEMATICS Geometry General. bisacsh Contact manifolds fast Differential equations, Nonlinear fast Meetkunde. gtt Niet-lineaire analyse. gtt Lychagin, V. V. (Valentin Vasilʹevich) https://id.oclc.org/worldcat/entity/E39PCjCWhVRhp6wPBM8b3cR7pP http://id.loc.gov/authorities/names/n85180906 Rubtsov, Vladimir, 1952- http://id.loc.gov/authorities/names/no2007032818 has work: Contact geometry and nonlinear differential equations (Text) https://id.oclc.org/worldcat/entity/E39PCGjdjmwQ3K7wDmqGvPtP6X https://id.oclc.org/worldcat/ontology/hasWork Print version: Kushner, Alexei. Contact geometry and non-linear differential equations 0521824761 (DLC) 2007273387 (OCoLC)60560104 Encyclopedia of mathematics and its applications ; volume 101. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616962 Volltext |
| spellingShingle | Kushner, Alexei Contact geometry and non-linear differential equations / Encyclopedia of mathematics and its applications ; Symmetries and integrals -- Distributions -- Ordinary differential equations -- Model differential equations and the lie superposition principle -- Symplectic algebra -- Linear algebra of symplectic vector spaces -- Exterior algebra on symplectic vector spaces -- A symplectic classification of exterior 2-forms in dimension 4 -- Symplectic classification of exterior 2-forms -- Classification of exterior 3-forms on a six-dimensional symplectic space -- Monge-Ampère equations -- Symplectic manifolds -- Contact manifolds -- Monge-Ampère equations -- Symmetries and contact transformations of Monge-Ampère equations -- Conservation laws -- Monge-Ampère equations on two-dimensional manifolds and geometric structures -- Systems of first-order partial differential equations on two-dimensional manifolds -- Applications -- Non-linear acoustics -- Non-linear thermal conductivity -- Meteorology applications -- Classification of Monge-Ampère equations -- Classification of symplectic MAOs on two-dimensional manifolds -- Classification of symplectic MAEs on two-dimensional manifolds -- Contact classification of MAEs on two-dimensional manifolds -- Symplectic classification of MAEs on three-dimensional manifolds. Contact manifolds. http://id.loc.gov/authorities/subjects/sh85031507 Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Variétés de contact (Géométrie) Équations différentielles non linéaires. MATHEMATICS Geometry General. bisacsh Contact manifolds fast Differential equations, Nonlinear fast Meetkunde. gtt Niet-lineaire analyse. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031507 http://id.loc.gov/authorities/subjects/sh85037906 |
| title | Contact geometry and non-linear differential equations / |
| title_alt | Contact geometry and nonlinear differential equations |
| title_auth | Contact geometry and non-linear differential equations / |
| title_exact_search | Contact geometry and non-linear differential equations / |
| title_full | Contact geometry and non-linear differential equations / Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov. |
| title_fullStr | Contact geometry and non-linear differential equations / Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov. |
| title_full_unstemmed | Contact geometry and non-linear differential equations / Alexei Kushner, Valentin Lychagin, and Vladimir Rubtsov. |
| title_short | Contact geometry and non-linear differential equations / |
| title_sort | contact geometry and non linear differential equations |
| topic | Contact manifolds. http://id.loc.gov/authorities/subjects/sh85031507 Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Variétés de contact (Géométrie) Équations différentielles non linéaires. MATHEMATICS Geometry General. bisacsh Contact manifolds fast Differential equations, Nonlinear fast Meetkunde. gtt Niet-lineaire analyse. gtt |
| topic_facet | Contact manifolds. Differential equations, Nonlinear. Variétés de contact (Géométrie) Équations différentielles non linéaires. MATHEMATICS Geometry General. Contact manifolds Differential equations, Nonlinear Meetkunde. Niet-lineaire analyse. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616962 |
| work_keys_str_mv | AT kushneralexei contactgeometryandnonlineardifferentialequations AT lychaginvv contactgeometryandnonlineardifferentialequations AT rubtsovvladimir contactgeometryandnonlineardifferentialequations |