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

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

2009-03-22

arxiv.org/abs/0903.3626v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

29 pages, 12 figures. To appear in Studies in Applied Mathematics

Scientific paper

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.

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