The Problem of Integrable Discretization: Hamiltonian Approach:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2003
|
| Schriftenreihe: | Progress in Mathematics
219 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The book explores the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Among several possible approaches to this theory, the Hamiltonian one is chosen as the guiding principle. A self-contained exposition of the Hamiltonian (r-matrix, or "Leningrad") approach to integrable systems is given, culminating in the formulation of a general recipe for integrable discretization of r-matrix hierarchies. After that, a detailed systematic study is carried out for the majority of known discrete integrable systems which can be considered as discretizations of integrable ordinary differential or differential-difference (lattice) equations. This study includes, in all cases, a unified treatment of the correspondent continuous integrable systems as well. The list of systems treated in the book includes, among others: Toda and Volterra lattices along with their numerous generalizations (relativistic, multi-field, Lie-algebraic, etc.), Ablowitz-Ladik hierarchy, peakons of the Camassa-Holm equation, Garnier and Neumann systems with their various relatives, many-body systems of the Calogero-Moser and Ruijsenaars-Schneider type, various integrable cases of the rigid body dynamics. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems. Also those involved in real numerical calculations or modelling with integrable systems will find it very helpful |
| Beschreibung: | 1 Online-Ressource (XXI, 1070 p) |
| ISBN: | 9783034880169 9783034894043 |
| DOI: | 10.1007/978-3-0348-8016-9 |
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| 500 | |a The book explores the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Among several possible approaches to this theory, the Hamiltonian one is chosen as the guiding principle. A self-contained exposition of the Hamiltonian (r-matrix, or "Leningrad") approach to integrable systems is given, culminating in the formulation of a general recipe for integrable discretization of r-matrix hierarchies. | ||
| 500 | |a After that, a detailed systematic study is carried out for the majority of known discrete integrable systems which can be considered as discretizations of integrable ordinary differential or differential-difference (lattice) equations. This study includes, in all cases, a unified treatment of the correspondent continuous integrable systems as well. The list of systems treated in the book includes, among others: Toda and Volterra lattices along with their numerous generalizations (relativistic, multi-field, Lie-algebraic, etc.), Ablowitz-Ladik hierarchy, peakons of the Camassa-Holm equation, Garnier and Neumann systems with their various relatives, many-body systems of the Calogero-Moser and Ruijsenaars-Schneider type, various integrable cases of the rigid body dynamics. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. | ||
| 500 | |a It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems. Also those involved in real numerical calculations or modelling with integrable systems will find it very helpful | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Suris, Yuri B. |
| author_facet | Suris, Yuri B. |
| author_role | aut |
| author_sort | Suris, Yuri B. |
| author_variant | y b s yb ybs |
| building | Verbundindex |
| bvnumber | BV042422011 |
| classification_tum | MAT 000 |
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| dewey-full | 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.33 |
| dewey-search | 511.33 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8016-9 |
| format | Electronic eBook |
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| id | DE-604.BV042422011 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034880169 9783034894043 |
| language | English |
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| spelling | Suris, Yuri B. Verfasser aut The Problem of Integrable Discretization: Hamiltonian Approach by Yuri B. Suris Basel Birkhäuser Basel 2003 1 Online-Ressource (XXI, 1070 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 219 The book explores the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Among several possible approaches to this theory, the Hamiltonian one is chosen as the guiding principle. A self-contained exposition of the Hamiltonian (r-matrix, or "Leningrad") approach to integrable systems is given, culminating in the formulation of a general recipe for integrable discretization of r-matrix hierarchies. After that, a detailed systematic study is carried out for the majority of known discrete integrable systems which can be considered as discretizations of integrable ordinary differential or differential-difference (lattice) equations. This study includes, in all cases, a unified treatment of the correspondent continuous integrable systems as well. The list of systems treated in the book includes, among others: Toda and Volterra lattices along with their numerous generalizations (relativistic, multi-field, Lie-algebraic, etc.), Ablowitz-Ladik hierarchy, peakons of the Camassa-Holm equation, Garnier and Neumann systems with their various relatives, many-body systems of the Calogero-Moser and Ruijsenaars-Schneider type, various integrable cases of the rigid body dynamics. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems. Also those involved in real numerical calculations or modelling with integrable systems will find it very helpful Mathematics Algebra Differentiable dynamical systems Computer science / Mathematics Order, Lattices, Ordered Algebraic Structures Dynamical Systems and Ergodic Theory Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Numerical and Computational Physics Solid State Physics Informatik Mathematik Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Integrables System (DE-588)4114032-1 gnd rswk-swf Integrables System (DE-588)4114032-1 s Hamilton-Formalismus (DE-588)4376155-0 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8016-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Suris, Yuri B. The Problem of Integrable Discretization: Hamiltonian Approach Mathematics Algebra Differentiable dynamical systems Computer science / Mathematics Order, Lattices, Ordered Algebraic Structures Dynamical Systems and Ergodic Theory Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Numerical and Computational Physics Solid State Physics Informatik Mathematik Hamilton-Formalismus (DE-588)4376155-0 gnd Integrables System (DE-588)4114032-1 gnd |
| subject_GND | (DE-588)4376155-0 (DE-588)4114032-1 |
| title | The Problem of Integrable Discretization: Hamiltonian Approach |
| title_auth | The Problem of Integrable Discretization: Hamiltonian Approach |
| title_exact_search | The Problem of Integrable Discretization: Hamiltonian Approach |
| title_full | The Problem of Integrable Discretization: Hamiltonian Approach by Yuri B. Suris |
| title_fullStr | The Problem of Integrable Discretization: Hamiltonian Approach by Yuri B. Suris |
| title_full_unstemmed | The Problem of Integrable Discretization: Hamiltonian Approach by Yuri B. Suris |
| title_short | The Problem of Integrable Discretization: Hamiltonian Approach |
| title_sort | the problem of integrable discretization hamiltonian approach |
| topic | Mathematics Algebra Differentiable dynamical systems Computer science / Mathematics Order, Lattices, Ordered Algebraic Structures Dynamical Systems and Ergodic Theory Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Numerical and Computational Physics Solid State Physics Informatik Mathematik Hamilton-Formalismus (DE-588)4376155-0 gnd Integrables System (DE-588)4114032-1 gnd |
| topic_facet | Mathematics Algebra Differentiable dynamical systems Computer science / Mathematics Order, Lattices, Ordered Algebraic Structures Dynamical Systems and Ergodic Theory Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Numerical and Computational Physics Solid State Physics Informatik Mathematik Hamilton-Formalismus Integrables System |
| url | https://doi.org/10.1007/978-3-0348-8016-9 |
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