The Problem of Integrable Discretization: Hamiltonian approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel [u.a.]
Birkhäuser
2003
|
| Series: | Progress in mathematics
219 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 1070 S. |
| ISBN: | 3764369957 |
Staff View
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| 100 | 1 | |a Suris, Yuri B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Problem of Integrable Discretization |b Hamiltonian approach |c Yuri B. Suris |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2003 | |
| 300 | |a XXI, 1070 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 219 | |
| 650 | 4 | |a Physique mathématique | |
| 650 | 7 | |a Sistemas dinâmicos |2 larpcal | |
| 650 | 7 | |a Sistemas hamiltonianos |2 larpcal | |
| 650 | 4 | |a Systèmes hamiltoniens | |
| 650 | 4 | |a Théories non linéaires | |
| 650 | 4 | |a Équations aux dérivées partielles - Solutions numériques | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 0 | 7 | |a Integrables System |0 (DE-588)4114032-1 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804130160900833280 |
|---|---|
| adam_text | Contents
Preface
I General Theory
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.11.1
1.11.2
1.12
1.12.1
1.12.2
1.13
1.13.1
1.13.2
A Appendix: Gradients, vector fields, and other notation
В
1.14
2
2.1
2.2
2.2.1
2.2.2
VI
Contents
2.2.3
2.3
2.3.1
2.3.2
2.3.3
2.4
2.5
2.5.1
2.5.2
2.5.3
2.6
2.6.1
2.6.2
2.6.3
2.7
2.8
2.9
A Appendix:
2.10
II Lattice Systems
3
3.1
3.2
3.3
3.3.1
3.3.2
3.4
3.5
3.6
3.7 2x2
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
Contents
VII
3.20
3.21
A Appendix: Miura transformations for KdV
3.22
Voiterra Lattice
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
A Appendix: Tower of modifications of VL
4.26
Newtonian Equations of the
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
Vlil
Contents
Relativistic
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9 2x2
6.10
6.11
6.12
6.13
6.14
6.15
6.15.1
6.15.2
6.16
6.16.1
6.16.2
6.17
6.18
6.18.1
6.18.2
6.19
6.20
6.21
Relativistic Volterra Lattice
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
Contents
7.14
7.15
7.16
7.16.1
7.16.2
7.16.3
7.17
Newtonian Equations of the Relativistic
8.1
8.2
8.2.1
8.2.2
Parametrizing the linear bracket
8.3.1
8.3.2
Dual linear parametrization
8.4.1
8.4.2
Parametrizing the quadratic bracket
8.5.1
8.5.2
Parametrizing the linear-quadratic bracket II
8.6.1
8.6.2
Parametrizing the cubic-quadratic bracket
Parametrizing the cubic bracket I
Parametrizing the cubic bracket II
Parametrizing the cubic bracket III
Bibliographical remarks
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
Explicit Discretizations for
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
Contents
10
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
12
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10
12.11
12.12
13
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
Сол
13.9
ι(α)
51
13.10
13.11
13.12
771+1
[a)
14
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10
14.11
14.12
15
15.3
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
15.10
15.11
15.12
15.13
15.14
■field Volterra-like Systems
Introduction
Multi-field analog of the Volterra lattice
Quadratic r-matrix structure for VLm
Discretization of VLm
Localizing change of variables for dVLm
Example
A further generalization of VLm
Quadratic r-matrix structure for VL,n
Discretization of VLm
Localizing change of variables for
Thecaseof the signatureCT
15.11.1
lS.ll^Discretization
15.11.3
15.1
Example
Example
Bibliographical remarks
16
16.1
16.2
16.3
16.4
16.5
Xli
Contents
16.6
16.7
16.8
16.8.1
16.8.2
16.8.3
16.8.4
of the relativistic Volterra lattice
16.9
16.9.1
16.9.2
16.9.3
16.10
16.11
17
17.1
17.2
17.3
17.4
17.5
17.5.1
17.5.2
17.6
17.7
17.8
17.9
17.10
17.11
17.12
17.13
18
18.1
18.2
18.3
18.4
18.4.1
18.4.2
18.5
18.6
18.7
18.8
18.9
Contents
xi
18.10
18.11
18.12
III Systems of Classical Mechanics
19
19.1
19.2
19.3
19.4
19.5
20
20.1
20.2
20.3
20.4
21
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9 2
21.10 2
21.11
21.12
21.13
21.14
22
22.1
22.2
22.2.1
22.2.2
22.2.3
22.2.4
22.3
22.3.1
22.3.2
XIV
Contents
22.3.3 Big Lax
22.3.4
22.4
22.4.1
22.4.2
22.4.3
22.4.4
22.5 Bäcklund
22.6 Bäcklund
22.7 Bäcklund
22.8
22.8.1
22.8.2
22.8.3
22.8.4
22.9
22.9.1
22.9.2
22.9.3
22.9.4
22.10
22.10.1
22.10.2
22.10.3
22.10.4
22.11
23
23.1
23.2
23.3
23.4
24
24.1
24.2
24.2.1
24.2.2
24.2.3
24.2.4
24.3
24.3.1
24.3.2
24.3.3
24.3.4
Contents
xv
24.4
24.4.1
24.4.2
24.4.3
24.4.4
24.5 Bäcklund
24.6 Bäcklund
24.7 Bäcklund
24.8
24.9
24.10
24.11
24.11.1
24.11.2Discretizationàla
24.12
25
25.1
25.2
25.3
25.3.1
25.3.2
25.3.3
25.3.4
25.4
25.5
25.5.1
25.5.2
25.6
26
26.1
26.2
26.3
26.4
26.5
26.6
26.6.1
26.6.2
26.7
26.7.1
26.7.2
26.8
26.9
26.10
xvi Contents
26.11
26.11.1
26.11.2
A Appendix:
26.12
27
27.1
27.2
27.3
27.4
27.4.1
27.4.2
27.5
27.5.1
27.5.2
27.6
27.6.1
27.6.2
27.7
27.8
27.9
27.10
27.10.1
27.10.2
27.11
Bibliography
List of Notations
Index
|
| any_adam_object | 1 |
| author | Suris, Yuri B. |
| author_facet | Suris, Yuri B. |
| author_role | aut |
| author_sort | Suris, Yuri B. |
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| dewey-search | 514/.74 |
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| id | DE-604.BV017323057 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:16:37Z |
| institution | BVB |
| isbn | 3764369957 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010441706 |
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| physical | XXI, 1070 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Suris, Yuri B. Verfasser aut The Problem of Integrable Discretization Hamiltonian approach Yuri B. Suris Basel [u.a.] Birkhäuser 2003 XXI, 1070 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 219 Physique mathématique Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Systèmes hamiltoniens Théories non linéaires Équations aux dérivées partielles - Solutions numériques Mathematische Physik Differential equations, Partial Numerical solutions Hamiltonian systems Mathematical physics Nonlinear theories Integrables System (DE-588)4114032-1 gnd rswk-swf Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Integrables System (DE-588)4114032-1 s Hamilton-Formalismus (DE-588)4376155-0 s DE-604 Progress in mathematics 219 (DE-604)BV000004120 219 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441706&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Suris, Yuri B. The Problem of Integrable Discretization Hamiltonian approach Progress in mathematics Physique mathématique Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Systèmes hamiltoniens Théories non linéaires Équations aux dérivées partielles - Solutions numériques Mathematische Physik Differential equations, Partial Numerical solutions Hamiltonian systems Mathematical physics Nonlinear theories Integrables System (DE-588)4114032-1 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4376155-0 |
| 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 Yuri B. Suris |
| title_fullStr | The Problem of Integrable Discretization Hamiltonian approach Yuri B. Suris |
| title_full_unstemmed | The Problem of Integrable Discretization Hamiltonian approach Yuri B. Suris |
| title_short | The Problem of Integrable Discretization |
| title_sort | the problem of integrable discretization hamiltonian approach |
| title_sub | Hamiltonian approach |
| topic | Physique mathématique Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Systèmes hamiltoniens Théories non linéaires Équations aux dérivées partielles - Solutions numériques Mathematische Physik Differential equations, Partial Numerical solutions Hamiltonian systems Mathematical physics Nonlinear theories Integrables System (DE-588)4114032-1 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd |
| topic_facet | Physique mathématique Sistemas dinâmicos Sistemas hamiltonianos Systèmes hamiltoniens Théories non linéaires Équations aux dérivées partielles - Solutions numériques Mathematische Physik Differential equations, Partial Numerical solutions Hamiltonian systems Mathematical physics Nonlinear theories Integrables System Hamilton-Formalismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441706&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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