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

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 introduction of additional independent variables. Algebraic conditions associated with the first-order central extension with respect to additional independent variables are derived. As a 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.