孤立波相互作用中的混沌散射：奇异迭代映射描述
Chaotic scattering in solitary wave interactions: A singular iterated-map description
摘要：
我们推导出一个家庭的奇异迭代映射-密切相关的庞加莱映射-描述碰撞孤立波之间的混沌相互作用。这种孤立波碰撞的混沌行为取决于能量转移到次级振荡模式，通常是脉冲的内部模式。与以前的分析不同，这张图允许人们理解这种模式在第一次碰撞之前被激发的情况下的相互作用。该地图是使用Melnikov积分和匹配的渐近展开和推广的"多脉冲“Melnikov积分，并允许一个找到不仅多脉冲异宿轨道，但奇异的周期轨道。导出的映射族表现出奇异行为，包括无限缠绕的区域。这个问题被证明是一个奇异版本的保守的池田地图从激光物理和连接的天体力学和流体力学的问题。
英文摘要：
We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. Unlike previous analyses, this map allows one to understand the interactions in the case when this mode is excited prior to the first collision. The map is derived using Melnikov integrals and matched asymptotic expansions and generalizes a ``multi-pulse'' Melnikov integral and allows one to find not only multipulse heteroclinic orbits, but exotic periodic orbits. The family of maps derived exhibits singular behavior, including regions of infinite winding. This problem is shown to be a singular version of the conservative Ikeda map from laser physics and connections are made with problems from celestial mechanics and fluid mechanics.
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