Separatrix Map Analysis for Fractal Scatterings in Weak Interactions of Solitary Waves
Exactly Solvable and Integrable Systems
2012-10-19 v1 Chaotic Dynamics
Pattern Formation and Solitons
Abstract
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.
Keywords
Cite
@article{arxiv.0903.3626,
title = {Separatrix Map Analysis for Fractal Scatterings in Weak Interactions of Solitary Waves},
author = {Yi Zhu and Richard Haberman and Jianke Yang},
journal= {arXiv preprint arXiv:0903.3626},
year = {2012}
}
Comments
29 pages, 12 figures. To appear in Studies in Applied Mathematics