Separatrix Map Analysis for Fractal Scatterings in Weak Interactions of Solitary Waves

Autor:	Zhu, Yi, Haberman, Richard, Yang, Jianke
Rok vydání:	2009
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Nonlinear Sciences - Chaotic Dynamics Nonlinear Sciences - Pattern Formation and Solitons
Druh dokumentu:	Working Paper
DOI:	10.1111/j.1467-9590.2009.00442.x
Popis:	Previous studies have shown that fractal scatterings in weak interactions of solitary waves in the generalized nonlinear Schr\"odinger 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. Comment: 29 pages, 12 figures. To appear in Studies in Applied Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0903.3626 Zobrazit plný text záznamu View this record from Arxiv