Unitized Jordan algebras and dispersionless KdV equations

McCarthy, O.D. and Strachan, I.A.B. (2001) Unitized Jordan algebras and dispersionless KdV equations. Journal of Physics A: Mathematical and General, 34(11), pp. 2435-2442. (doi: 10.1088/0305-4470/34/11/332)

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. Recursion laws for conserved densities are given under the assumption that the algebra possesses a unity element. Sufficient conditions are given for the unitized counterpart of a diagonalizable non-unital system to be diagonalizable. Hamiltonian structure is discussed within the context of D_N Jordan algebras and CP^N scattering problems.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Strachan, Professor Ian
• Authors: McCarthy, O.D., and 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 Physics A: Mathematical and General
• Publisher: Institute of Physics Publishing Ltd.
• ISSN: 0305-4470