Radiationless energy exchange in three-soliton collisions

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.

11 pages, 14 figures, submitted for publication

References in corpus (3)

• Two-soliton collisions in a near-integrable lattice system
• Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations
• A Universal Map for Fractal Structures in Weak Solitary Wave Interactions

Cited by in corpus (13)

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• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• High energy density in multi-soliton collisions
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Collision of ${\varphi }^4$ kinks free of the Peierls-Nabarro barrier in the regime of strong discreteness
• Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities
• Resonant interaction of ${\varphi }^4$ kink with spatially periodic $\mathcal{P}\mathcal{T}$-symmetric perturbation
• Double sine-Gordon class of universal coarsening dynamics in a spin-1 Bose gas
• Excitation of high-amplitude localized nonlinear waves as a result of interaction of kink with attractive impurity in sine-Gordon equation
• Kink dynamics in a high-order field model
• Dynamics of localized solutions in three core coupled waveguides with quasi-periodic nonlinearity