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Jordan manifolds and dispersionless KdV equations

Strachan, I.A.B. (2000) Jordan manifolds and dispersionless KdV equations. Journal of Nonlinear Mathematical Physics, 7 (4). pp. 495-510. ISSN 1402-9251 (doi:10.2991/jnmp.2000.7.4.7)

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Publisher's URL: http://dx.doi.org/10.2991/jnmp.2000.7.4.7

Abstract

Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order symmetries, recursion operators and hierarchies of conservation laws. In this paper the dispersionless limits of these Jordan KdV equations are studied, under the assumptions that the Jordan algebra has a unity element and a compatible non-degenerate inner product. Much of this structure may be encoded in a so-called Jordan manifold, akin to a Frobenius manifold. In particular the Hamiltonian properties of these systems are investigated.

Item Type:Article
Status:Published
Refereed:Yes
Glasgow Author(s):Strachan, Prof Ian
Authors: Strachan, I.A.B.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Nonlinear Mathematical Physics
Publisher:Atlantis Press
ISSN:1402-9251
ISSN (Online):1776-0852
Copyright Holders:Copyright © 2000 Atlantis Press and The Author
First Published:First published in Journal Of Nonlinear Mathematical Physics 7(4):495-510
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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