Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters

Nimmo, J.J.C. and Ruijsenaars, S.N.M. (2009) Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters. Journal of Mathematical Physics, 50(4), 043511. (doi: 10.1063/1.3110012)

Abstract

We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the 6N-dimensional phase space Omega of the relativistic systems with 2N particles and N antiparticles, there exists a 2N-dimensional Poincaré-invariant submanifold OmegaP corresponding to N free particles and N bound particle-antiparticle pairs in their ground state. The Tzitzeica N-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of OmegaP. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Nimmo, Dr Jonathan
• Authors: Nimmo, J.J.C., and Ruijsenaars, S.N.M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Mathematical Physics
• Journal Abbr.: J. Math. Phys.
• Publisher: American Institute of Physics
• ISSN: 0022-2488
• ISSN (Online): 1089-7658
• Copyright Holders: Copyright © 2009 American Institute of Physics
• First Published: First published in Journal of Mathematical Physics 50(4):043511
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.