Discrete systems and integrability:
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2016
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| Schriftenreihe: | Cambridge texts in applied mathematics
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 06 Sep 2016) |
| Beschreibung: | 1 online resource (xiii, 445 pages) |
| ISBN: | 9781107337411 |
| DOI: | 10.1017/CBO9781107337411 |
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| 500 | |a Title from publisher's bibliographic system (viewed on 06 Sep 2016) | ||
| 505 | 8 | |a Introduction to difference equations -- Discrete equations from transformations of continuous equations -- Integrability of PEs -- Interlude: lattice equations and numerical algorithms -- Continuum limits of lattice PE -- One-dimensional lattices and maps -- Identifying integrable difference equations -- Hirota's bilinear method -- Multi-soliton solutions and the Cauchy matrix scheme -- Similarity reductions of integrable PE's -- Discrete Painlevé equations -- Lagrangian multiform theory | |
| 520 | |a This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Integral equations | |
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| 700 | 1 | |a Joshi, Nalini |e Sonstige |0 (DE-588)1114428825 |4 oth | |
| 700 | 1 | |a Nijhoff, Frank W. |e Sonstige |0 (DE-588)1114428884 |4 oth | |
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Datensatz im Suchindex
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| author | Hietarinta, J. |
| author_GND | (DE-588)1114428728 (DE-588)1114428825 (DE-588)1114428884 |
| author_facet | Hietarinta, J. |
| author_role | aut |
| author_sort | Hietarinta, J. |
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| building | Verbundindex |
| bvnumber | BV043940080 |
| collection | ZDB-20-CBO |
| contents | Introduction to difference equations -- Discrete equations from transformations of continuous equations -- Integrability of PEs -- Interlude: lattice equations and numerical algorithms -- Continuum limits of lattice PE -- One-dimensional lattices and maps -- Identifying integrable difference equations -- Hirota's bilinear method -- Multi-soliton solutions and the Cauchy matrix scheme -- Similarity reductions of integrable PE's -- Discrete Painlevé equations -- Lagrangian multiform theory |
| ctrlnum | (ZDB-20-CBO)CR9781107337411 (OCoLC)967678444 (DE-599)BVBBV043940080 |
| dewey-full | 511/.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.1 |
| dewey-search | 511/.1 |
| dewey-sort | 3511 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107337411 |
| format | Electronic eBook |
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| id | DE-604.BV043940080 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:12Z |
| institution | BVB |
| isbn | 9781107337411 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349050 |
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| physical | 1 online resource (xiii, 445 pages) |
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| publishDate | 2016 |
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| publisher | Cambridge University Press |
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| series2 | Cambridge texts in applied mathematics |
| spelling | Hietarinta, J. Verfasser (DE-588)1114428728 aut Discrete systems and integrability J. Hietarinta, N. Joshi, F.W. Nijhoff Cambridge Cambridge University Press 2016 1 online resource (xiii, 445 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge texts in applied mathematics Title from publisher's bibliographic system (viewed on 06 Sep 2016) Introduction to difference equations -- Discrete equations from transformations of continuous equations -- Integrability of PEs -- Interlude: lattice equations and numerical algorithms -- Continuum limits of lattice PE -- One-dimensional lattices and maps -- Identifying integrable difference equations -- Hirota's bilinear method -- Multi-soliton solutions and the Cauchy matrix scheme -- Similarity reductions of integrable PE's -- Discrete Painlevé equations -- Lagrangian multiform theory This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines Mathematische Physik Integral equations Mathematical physics Joshi, Nalini Sonstige (DE-588)1114428825 oth Nijhoff, Frank W. Sonstige (DE-588)1114428884 oth Erscheint auch als Druckausgabe 978-1-107-04272-8 Erscheint auch als Druckausgabe 978-1-107-66948-2 https://doi.org/10.1017/CBO9781107337411 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hietarinta, J. Discrete systems and integrability Introduction to difference equations -- Discrete equations from transformations of continuous equations -- Integrability of PEs -- Interlude: lattice equations and numerical algorithms -- Continuum limits of lattice PE -- One-dimensional lattices and maps -- Identifying integrable difference equations -- Hirota's bilinear method -- Multi-soliton solutions and the Cauchy matrix scheme -- Similarity reductions of integrable PE's -- Discrete Painlevé equations -- Lagrangian multiform theory Mathematische Physik Integral equations Mathematical physics |
| title | Discrete systems and integrability |
| title_auth | Discrete systems and integrability |
| title_exact_search | Discrete systems and integrability |
| title_full | Discrete systems and integrability J. Hietarinta, N. Joshi, F.W. Nijhoff |
| title_fullStr | Discrete systems and integrability J. Hietarinta, N. Joshi, F.W. Nijhoff |
| title_full_unstemmed | Discrete systems and integrability J. Hietarinta, N. Joshi, F.W. Nijhoff |
| title_short | Discrete systems and integrability |
| title_sort | discrete systems and integrability |
| topic | Mathematische Physik Integral equations Mathematical physics |
| topic_facet | Mathematische Physik Integral equations Mathematical physics |
| url | https://doi.org/10.1017/CBO9781107337411 |
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