Chaotic scattering in solitary wave interactions: a singular iterated-map description.
Chaotic scattering in solitary wave interactions: a singular iterated-map description.
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DOI：
10.1063/1.2904823
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发表时间：
2007-10
期刊：
影响因子：
2.9
通讯作者：
Roy H. Goodman
中科院分区：
文献类型：
--
作者：
Roy H. Goodman
我们导出了一组奇异迭代映射——与庞加莱映射密切相关——它们描述了碰撞孤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向次级振荡模式的转移，通常是脉冲的内部模式。这张图使我们能够超越以前的分析，并理解在这种模式在第一次碰撞之前被激发的情况下的相互作用。利用Melnikov积分和匹配渐近展开式导出映射，推广了“多脉冲”Melnikov积分。它不仅能发现多脉冲异斜轨道，还能发现奇异的周期轨道。这些地图表现出奇异的行为，包括无限缠绕的区域。这些图被证明是激光物理学中保守的池田图的奇异版本，并与天体力学和流体力学的问题联系起来。
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. This map allows us to go beyond previous analyses and 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 "multipulse" Melnikov integral. It allows one to find not only multipulse heteroclinic orbits, but exotic periodic orbits. The maps exhibit singular behavior, including regions of infinite winding. These maps are shown to be singular versions of the conservative Ikeda map from laser physics and connections are made with problems from celestial mechanics and fluid mechanics.