Integrable Particle Systems vs Solutions to the KP and 2D Toda Equations

✍ Scribed by S.N.M. Ruijsenaars

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 730 KB
• Volume: 256
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1997.5674

✦ Synopsis

Starting from the relation between integrable relativistic N-particle systems with hyperbolic interactions and elementary N-soliton solutions to the KP and 2D Toda equations, we show how fusion properties of the soliton solutions are mirrored by fusion properties of the Poisson commuting particle dynamics. We also obtain previously known relations between elliptic solutions and integrable N-particle systems with elliptic interactions, without invoking finitegap integration theory. 1997 Academic Press CONTENTS 1. Introduction and summary. 2. Soliton {-functions: Asymptotics and fusion. 3. II rel particles vs elementary solitons. 4. Bound particle antiparticle pairs vs s 2 -solitons. 5. The s n -soliton case. 6. Interlude: The III b molecule. 7. The general case. Appendixes. A. Toda solitons revisited. B. IV rel particles vs 2D Toda solutions. C. II nr and IV nr particles vs KP solutions. D. Some functional identities. E. The equal-n j transform.