The sine-Gordon solitons as an N-body problem

Olivier Babelon (1) , Denis Bernard

1 SPhT - Service de Physique Théorique

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.

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Olivier Babelon, Denis Bernard. The sine-Gordon solitons as an N-body problem. Physics Letters B, 1993, 317 (3), pp.363-368. ⟨10.1016/0370-2693(93)91009-C⟩. ⟨hal-03370720⟩