孤立波弱相互作用分形散射的分界线映射分析
Separatrix Map Analysis for Fractal Scatterings in Weak Interactions of Solitary Waves
摘要：
已有的研究表明，广义非线性薛定谔方程中孤立波弱相互作用的分形散射可用一个普适的二阶分界线映射来描述。本文详细分析了这种分界线映射，从而得到了这些弱相互作用中分形散射的完整刻画。特别是，对于不同的初始条件，解析推导出这些分形的标度律，并通过直接数值模拟证实了这些定律。此外，一个分析准则的分形散射的发生明确给出。
英文摘要：
Previous studies have shown that fractal scatterings in weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are described by a universal second-order separatrix map. In this paper, this separatrix map is analyzed in detail, and hence a complete characterization of fractal scatterings in these weak interactions is obtained. In particular, scaling laws of these fractals are derived analytically for different initial conditions, and these laws are confirmed by direct numerical simulations. In addition, an analytical criterion for the occurrence of fractal scatterings is given explicitly.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
