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. (doi: 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: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Strachan, Professor 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.