The sine-Gordon solitons as an N-body problem

1993/09/28 by O. Babelon, Olivier Babelon, Denis Bernard · 91 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Generalization #Geometry #Integrable system #Lax pair #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Monodromy matrix #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Poisson bracket #Pure mathematics #Quadratic equation #Quantum mechanics #Sine #Soliton #hep-th #sine-Gordon equation

paper · pdf · doi:10.1016/0370-2693(93)91009-c

published in Physics Letters B 317(3), 363-368 (Elsevier BV) · 10 pages LATEX SPhT-93-072; LPTHE-93-40

arxiv created 1993/09/28 · openalex publication_date 1993/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the N-soliton solutions in the sine-Gordon model as a N-body problem. This leads to a relativistic generalization of the Calogero model first introduced by Ruijsenaars. We show that the fundamental Poisson bracket of the Lax matrix is quadratic, and the r-matrix is a dynamical one. This is in contrast to the Calogero model where the fundamental Poisson bracket of the Lax matrix is linear.

Citations

• Exchange operator formalism for integrable systems of particles
• Explicit Solution to the N-Body Calogero Problem
• Differential-difference operators associated to reflection groups
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Cited by

• Self-Duality and Scattering Map for the Hyperbolic van Diejen Systems with Two Coupling Parameters (with an Appendix by S. Ruijsenaars)