The Sine-Gordon Solitons as a N-Body Problem
Olivier Babelon, Denis Bernard
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.
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