Integrable Boundary for Quad-Graph Systems: Three-Dimensional Boundary Consistency
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Integrable Boundary for Quad-Graph Systems: Three-Dimensional Boundary Consistency
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| Creator |
Caudrelier, V.
Crampé, N. Zhang, Q.C. |
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| Description |
We propose the notion of integrable boundary in the context of discrete integrable systems on quad-graphs. The equation characterizing the boundary must satisfy a compatibility equation with the one characterizing the bulk that we called the three-dimensional (3D) boundary consistency. In comparison to the usual 3D consistency condition which is linked to a cube, our 3D boundary consistency condition lives on a half of a rhombic dodecahedron. The We provide a list of integrable boundaries associated to each quad-graph equation of the classification obtained by Adler, Bobenko and Suris. Then, the use of the term ''integrable boundary'' is justified by the facts that there are Bäcklund transformations and a zero curvature representation for systems with boundary satisfying our condition. We discuss the three-leg form of boundary equations, obtain associated discrete Toda-type models with boundary and recover previous results as particular cases. Finally, the connection between the 3D boundary consistency and the set-theoretical reflection equation is established.
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| Date |
2019-02-11T17:05:17Z
2019-02-11T17:05:17Z 2014 |
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| Type |
Article
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| Identifier |
Integrable Boundary for Quad-Graph Systems: Three-Dimensional Boundary Consistency / V. Caudrelier, N. Crampé, Q.C. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 30 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 05C10; 37K10; 39A12; 57M15 DOI:10.3842/SIGMA.2014.014 http://dspace.nbuv.gov.ua/handle/123456789/146841 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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