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

Yi Zhu Center for Applied Mathematics (ZCAM), Tsinghua University, Beijing 100084, China Richard Haberman Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA Jianke Yang Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, USA

arXiv subject: Exactly Solvable and Integrable Systems (nlin.SI) mathscidoc:2204.71001

2009.3
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.
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@inproceedings{yi2009separatrix,
  title={Separatrix Map Analysis for Fractal Scatterings in Weak Interactions of Solitary Waves},
  author={Yi Zhu, Richard Haberman, and Jianke Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421104659003535076},
  year={2009},
}
Yi Zhu, Richard Haberman, and Jianke Yang. Separatrix Map Analysis for Fractal Scatterings in Weak Interactions of Solitary Waves. 2009. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421104659003535076.
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