Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras

Symmetry Integrability and Geometry-Methods and Applications

article

Błażej M. Szablikowski¹ 

[1] Faculty of Physics, Division of Mathematical Physics, Adam Mickiewicz University

关键词: Novikov algebras;    (2 + 1)- and (3 + 1)-dimensional integrable systems;    bi-Hamiltonian structures;    central extensions;   

DOI  :  10.3842/SIGMA.2019.094

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown