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Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras
Blażej M. Szablikowski Faculty of Physics, Division of Mathematical Physics, Adam Mickiewicz University, ul. Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland
Abstract:
The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84–117] are extended over consideration of central extensions allowing the introducing of additional independent variables. Algebraic conditions associated to the first-order central extension with respect to additional independent variables are derived. As result $(2+1)$- and, in principle, higher-dimensional multicomponent bi-Hamiltonian systems are constructed. Necessary classification of the central extensions for low-dimensional Novikov algebras is performed and the theory is illustrated by significant $(2+1)$- and $(3+1)$-dimensional examples.
Keywords:
Novikov algebras, $(2+1)$- and $(3+1)$-dimensional integrable systems, bi-Hamiltonian structures, central extensions.
Received: June 21, 2019; in final form November 21, 2019; Published online November 29, 2019
Citation:
Blażej M. Szablikowski, “Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras”, SIGMA, 15 (2019), 094, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1530 https://www.mathnet.ru/eng/sigma/v15/p94
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Abstract page: | 90 | Full-text PDF : | 19 | References: | 9 |
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