Universal Map for Fractal Structures in Weak Interactions of Solitary Waves

Yi Zhu, Richard Haberman, and Jianke Yang
Phys. Rev. Lett. 100, 143901 – Published 10 April 2008
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Abstract

Fractal scatterings in weak solitary-wave interactions are analyzed for generalized nonlinear Schrödiger equations (GNLS). Using asymptotic methods, these weak interactions are reduced to a universal second-order map. This map gives the same fractal-scattering patterns as those in the GNLS equations both qualitatively and quantitatively. Scaling laws of these fractals are also derived.

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  • Received 21 November 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.143901

©2008 American Physical Society

Authors & Affiliations

Yi Zhu1, Richard Haberman2, and Jianke Yang3

  • 1Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China
  • 2Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA
  • 3Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA

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Vol. 100, Iss. 14 — 11 April 2008

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