Novikov algebras and a classification of multicomponent Camassa-Holm equations

Strachan, I. B. and Szablikowski, B. M. (2014) Novikov algebras and a classification of multicomponent Camassa-Holm equations. Studies in Applied Mathematics, 133(1), pp. 84-117. (doi: 10.1111/sapm.12040)

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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. These multi-component bi-Hamiltonian systems obtained by this construction may be interpreted as Euler equations on the centrally extended Lie algebras associated to the Novikov algebras. The related bilinear forms generating cocycles of first, second and third order are classified. Several examples, including known integrable equations, are presented.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Szablikowski, Dr Blazej and Strachan, Professor Ian
Authors: Strachan, I. B., and Szablikowski, B. M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Studies in Applied Mathematics
Publisher:Wiley Periodicals, Inc.
ISSN (Online):1467-9590
Copyright Holders:Copyright © 2014 Massachusetts Institute of Technology
First Published:First published in Studies in Applied Mathematics 133(1):84-117
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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