Symmetries and integrability of difference equations:
Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
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| Schriftenreihe: | London Mathematical Society lecture note series
381 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xviii, 341 pages) |
| ISBN: | 9780511997136 |
| DOI: | 10.1017/CBO9780511997136 |
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| 505 | 8 | |a Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals / V. Dorodnitsyn and R. Kozlov -- Painlevé equations: continuous, discrete and ultradiscrete / B. Grammaticos and A. Ramani -- Definitions and predictions of integrability for difference equations / J. Hietarinta -- Orthogonal polynomials, their recursions, and functional equations / M.E.H. Ismail -- Discrete Painlevé equations and orthogonal polynomials / A. Its -- Generalized Lie symmetries for difference equations / D. Levi and R.I. Yamilov -- Four lectures on discrete systems / S.P. Novikov -- Lectures on moving frames / P.J. Olver -- Lattices of compact semisimple Lie groups / J. Patera -- Lectures on discrete differential geometry / Yu. B Suris -- Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations / P. Winternitz | |
| 520 | |a Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference | ||
| 650 | 4 | |a Difference equations | |
| 650 | 4 | |a Symmetry (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804176882653986816 |
|---|---|
| any_adam_object | |
| author2 | Levi, D. |
| author2_role | edt |
| author2_variant | d l dl |
| author_facet | Levi, D. |
| building | Verbundindex |
| bvnumber | BV043941240 |
| classification_rvk | SI 320 |
| collection | ZDB-20-CBO |
| contents | Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals / V. Dorodnitsyn and R. Kozlov -- Painlevé equations: continuous, discrete and ultradiscrete / B. Grammaticos and A. Ramani -- Definitions and predictions of integrability for difference equations / J. Hietarinta -- Orthogonal polynomials, their recursions, and functional equations / M.E.H. Ismail -- Discrete Painlevé equations and orthogonal polynomials / A. Its -- Generalized Lie symmetries for difference equations / D. Levi and R.I. Yamilov -- Four lectures on discrete systems / S.P. Novikov -- Lectures on moving frames / P.J. Olver -- Lattices of compact semisimple Lie groups / J. Patera -- Lectures on discrete differential geometry / Yu. B Suris -- Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations / P. Winternitz |
| ctrlnum | (ZDB-20-CBO)CR9780511997136 (OCoLC)852513929 (DE-599)BVBBV043941240 |
| dewey-full | 515/.625 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.625 |
| dewey-search | 515/.625 |
| dewey-sort | 3515 3625 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511997136 |
| format | Electronic eBook |
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| id | DE-604.BV043941240 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:15Z |
| institution | BVB |
| isbn | 9780511997136 |
| language | English |
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| spelling | Symmetries and integrability of difference equations edited by Decio Levi [and others] Symmetries & Integrability of Difference Equations Cambridge Cambridge University Press 2011 1 online resource (xviii, 341 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 381 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals / V. Dorodnitsyn and R. Kozlov -- Painlevé equations: continuous, discrete and ultradiscrete / B. Grammaticos and A. Ramani -- Definitions and predictions of integrability for difference equations / J. Hietarinta -- Orthogonal polynomials, their recursions, and functional equations / M.E.H. Ismail -- Discrete Painlevé equations and orthogonal polynomials / A. Its -- Generalized Lie symmetries for difference equations / D. Levi and R.I. Yamilov -- Four lectures on discrete systems / S.P. Novikov -- Lectures on moving frames / P.J. Olver -- Lattices of compact semisimple Lie groups / J. Patera -- Lectures on discrete differential geometry / Yu. B Suris -- Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations / P. Winternitz Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference Difference equations Symmetry (Mathematics) Integrals Symmetrie (DE-588)4058724-1 gnd rswk-swf Integrierbarkeit (DE-588)4474751-2 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1994 L'Estérel Québec gnd-content 2\p (DE-588)1071861417 Konferenzschrift 2008 Montréal gnd-content Differenzengleichung (DE-588)4012264-5 s Symmetrie (DE-588)4058724-1 s Integrierbarkeit (DE-588)4474751-2 s 3\p DE-604 Levi, D. edt Erscheint auch als Druckausgabe 978-0-521-13658-7 https://doi.org/10.1017/CBO9780511997136 Verlag URL des Erstveröffentlichers 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 |
| spellingShingle | Symmetries and integrability of difference equations Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals / V. Dorodnitsyn and R. Kozlov -- Painlevé equations: continuous, discrete and ultradiscrete / B. Grammaticos and A. Ramani -- Definitions and predictions of integrability for difference equations / J. Hietarinta -- Orthogonal polynomials, their recursions, and functional equations / M.E.H. Ismail -- Discrete Painlevé equations and orthogonal polynomials / A. Its -- Generalized Lie symmetries for difference equations / D. Levi and R.I. Yamilov -- Four lectures on discrete systems / S.P. Novikov -- Lectures on moving frames / P.J. Olver -- Lattices of compact semisimple Lie groups / J. Patera -- Lectures on discrete differential geometry / Yu. B Suris -- Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations / P. Winternitz Difference equations Symmetry (Mathematics) Integrals Symmetrie (DE-588)4058724-1 gnd Integrierbarkeit (DE-588)4474751-2 gnd Differenzengleichung (DE-588)4012264-5 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4474751-2 (DE-588)4012264-5 (DE-588)1071861417 |
| title | Symmetries and integrability of difference equations |
| title_alt | Symmetries & Integrability of Difference Equations |
| title_auth | Symmetries and integrability of difference equations |
| title_exact_search | Symmetries and integrability of difference equations |
| title_full | Symmetries and integrability of difference equations edited by Decio Levi [and others] |
| title_fullStr | Symmetries and integrability of difference equations edited by Decio Levi [and others] |
| title_full_unstemmed | Symmetries and integrability of difference equations edited by Decio Levi [and others] |
| title_short | Symmetries and integrability of difference equations |
| title_sort | symmetries and integrability of difference equations |
| topic | Difference equations Symmetry (Mathematics) Integrals Symmetrie (DE-588)4058724-1 gnd Integrierbarkeit (DE-588)4474751-2 gnd Differenzengleichung (DE-588)4012264-5 gnd |
| topic_facet | Difference equations Symmetry (Mathematics) Integrals Symmetrie Integrierbarkeit Differenzengleichung Konferenzschrift 1994 L'Estérel Québec Konferenzschrift 2008 Montréal |
| url | https://doi.org/10.1017/CBO9780511997136 |
| work_keys_str_mv | AT levid symmetriesandintegrabilityofdifferenceequations AT levid symmetriesintegrabilityofdifferenceequations |