Radiationless energy exchange in three-soliton collisions

TL;DR

This paper introduces a three-particle model to explain complex behaviors in three-soliton collisions within a weakly perturbed sine-Gordon system, including elasticity variations, fractal scattering, and bound states.

Contribution

The authors develop a novel effective three-particle model that captures key features of three-soliton collisions without involving internal kink modes.

Findings

Collisions between two kinks and one antikink can be elastic or inelastic depending on initial positions.

Collision elasticity increases with higher collision velocities.

The model qualitatively reproduces fractal scattering and short-lived bound states.

Abstract

We revisit the problem of the three-soliton collisions in the weakly perturbed sine-Gordon equation and develop an effective three-particle model allowing to explain many interesting features observed in numerical simulations of the soliton collisions. In particular, we explain why collisions between two kinks and one antikink are observed to be practically elastic or strongly inelastic depending on relative initial positions of the kinks. The fact that the three-soliton collisions become more elastic with an increase in the collision velocity also becomes clear in the framework of the three-particle model. The three-particle model does not involve internal modes of the kinks, but it gives a qualitative description to all the effects observed in the three-soliton collisions, including the fractal scattering and the existence of short-lived three-soliton bound states. The radiationless energy exchange between the colliding solitons in weakly perturbed integrable systems takes place in the vicinity of the separatrix multi-soliton solutions of the corresponding integrable equations, where even small perturbations can result in a considerable change in the collision outcome. This conclusion is illustrated through the use of the reduced three-particle model.