Amsterdam MANY - PARTICLE EFFECTS IN NEARLY INTEGRABLE SYSTEMS

For the sine-Gordon and nonlinear Schr~Sdinger equations with conservative perturbations three-particle effects in collision of a fast soliton with two more slow ones are considered in the first order of the perturbation theory. The momentum and energy exchanged between the fast soliton and slow ones are calculated. For the latter system the three-particle contribution to the perturbation-induced phase shift of the fast soliton is calculated too. The effects vanish when the overlapping between the slow solitons is absent at the collision moment. In the former system inelastic interaction between the fast kink and a weakly bound breather is considered. The threshold value of the breather's binding energy admitting breaking the breather into a kink-antikink pair is calculated. Analogously, the inelastic collision of two weakly bound breathers is considered. For the collision of two "relativistic" sine-Gordon kinks the energy radiated under the action of the conservative perturbation is found and is demonstrated to be asymptotically independent on the relative polarity of the kinks.