Szablikowski B.M. Novikov algebras and a classification of multicomponent Camassa-Holm equations, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)

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Speaker: Błażej Szablikowski

Title: Novikov algebras and a classification of multicomponent Camassa-Holm equations

Abstract:
A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by Bai and Meng. The multi-component equations under consideration are shown to be bi-Hamiltonian systems that can be interpreted as Euler equations on centrally extended Lie algebras associated to Novikov algebras. The related bilinear forms generating cocycles of first, second and third order are classified. Several examples, including known integrable equations, are provided. (It is a joint work with Ian Strachan from Glasgow University.)

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