THE SINE-GORDON SOLITONS AS AN N-BODY PROBLEM

We consider the N-soliton solutions in the sine-Gordon model as an N-b ody problem. This leads to a relativistic generalization of the Caloge ro 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 fu ndamental Poisson bracket of the Lax matrix is linear.