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Symmetries of the Continuous and Discrete Krichever-Novikov Equation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetries of the Continuous and Discrete Krichever-Novikov Equation
Інший ID:
2010 Mathematics Subject Classification: 35B06; 35K25; 37K10; 39A14
Посилання:
Symmetries of the Continuous and Discrete Krichever-Novikov Equation / D. Levi, P. Winternitz, R.I. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 31 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html.
The research of L.D. has been partly supported by the Italian Ministry of Education and Research, PRIN “Continuous and discrete nonlinear integrable evolutions: from water waves to symplectic maps”. The research of P.W. was partly supported by a research grant from NSERC of Canada. R.I.Y. has been partially supported by the Russian Foundation for Basic Research (grant numbers 10-01-00088-a and 11-01-97005-r-povolzhie-a).
Дата:
2011
Переглядів:
308
Завантажень:
198
Анотація:
A symmetry classification is performed for a class of differential-difference equations depending on 9 parameters. A 6-parameter subclass of these equations is an integrable discretization of the Krichever-Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1≤n≤5. The highest dimensions, namely n=5 and n=4 occur only in the integrable cases.
