Dmitriev Sergey V, Kevrekidis Panayotis G, Kivshar Yuri S
Institute for Metals Superplasticity Problems RAS, Khalturina 39, 450001 Ufa, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Oct;78(4 Pt 2):046604. doi: 10.1103/PhysRevE.78.046604. Epub 2008 Oct 9.
We revisit the problem of the three-soliton collisions in the weakly perturbed sine-Gordon equation and develop an effective three-particle model allowing us 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.
我们重新审视弱扰动正弦 - 戈登方程中的三孤子碰撞问题，并开发了一个有效的三粒子模型，使我们能够解释在孤子碰撞数值模拟中观察到的许多有趣特征。特别是，我们解释了为什么根据扭结的相对初始位置，观察到两个扭结和一个反扭结之间的碰撞实际上是弹性的或强烈非弹性的。在三粒子模型的框架内，三孤子碰撞随着碰撞速度的增加而变得更具弹性这一事实也变得清晰起来。三粒子模型不涉及扭结的内部模式，但它对三孤子碰撞中观察到的所有效应给出了定性描述，包括分形散射和短寿命三孤子束缚态的存在。在弱扰动可积系统中，碰撞孤子之间的无辐射能量交换发生在相应可积方程的分界线多孤子解附近，即使是很小的扰动也可能导致碰撞结果的相当大变化。通过使用简化的三粒子模型说明了这一结论。
