三孤子碰撞中的无辐射能量交换
Radiationless energy exchange in three-soliton collisions
摘要：
我们重新审视弱扰动sine-Gordon方程中的三孤子碰撞问题，并建立了一个有效的三粒子模型，可以解释孤子碰撞数值模拟中观察到的许多有趣的特征。特别是，我们解释了为什么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非弹性的，具体取决于扭结的相对初始位置。在三粒子模型的框架下，三孤子碰撞随着碰撞速度的增加而变得更有弹性的事实也变得清晰。三粒子模型不涉及扭结的内模，但对三孤子碰撞中观察到的所有效应，包括分形散射和短寿命三孤子束缚态的存在，给出了定性的描述。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，在那里即使很小的扰动也会导致碰撞结果的显著变化。这一结论是通过使用简化的三粒子模型说明。
英文摘要：
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.
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