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періодичних видань НАН України
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Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
Інший ID:
2010 Mathematics Subject Classification: 35Q53; 37K40
DOI: http://dx.doi.org/10.3842/SIGMA.2012.062
DOI: http://dx.doi.org/10.3842/SIGMA.2012.062
Посилання:
Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time / R. Garifullin, I. Habibullin, M. Yangubaeva // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 41 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Geometrical Methods in Mathematical Physics”. The full collection is available at http://www.emis.de/journals/SIGMA/GMMP2012.html.
The authors are grateful to the referees for their important contribution to improve the article. This work is partially supported by Russian Foundation for Basic Research (RFBR) grants 11-01-97005-r-povoljie-a, 12-01-31208-mol a and 10-01-00088-a and by Federal Task Program “Scientific and pedagogical staf f of innovative Russia for 2009–2013” contract no. 2012-1.5-12-000-1003-011.
Дата:
2012
Переглядів:
604
Завантажень:
226
Анотація:
Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras AN, BN, CN, G₂, D₃, A₁⁽¹⁾, A₂⁽²⁾, DN⁽²⁾ these systems are proved to be integrable. For the systems corresponding to the algebras A₂, A₁⁽¹⁾, A₂⁽²⁾ generalized symmetries are found. For the systems A₂, B₂, C₂, G₂, D₃ complete sets of independent integrals are found. The Lax representation for the difference-difference systems corresponding to AN, BN, CN, A₁⁽¹⁾,DN⁽²⁾ are presented.
