Miura transformations from Novikov algebras

Professor Ian Strachan, University of Glasgow. IS Seminar Series.

For the KdV equation, the Muira map transforms the second Hamiltonian structure into the first Hamiltonian structure. Multicomponent generalization of KdV’s bi-Hamiltonian structure have been known for decades – they date back to the work of Gelfand and Dorfman, and Balinskii and Novikov – and are defined in terms of algebraic structures known as Novikov algebras. The corresponding Muira map for these structures was constructed by Balinskii and Novikov only in the case where the algebra is commutative. In this talk a construction will be presented which solves the problem of the construction of these maps in general.