Universal Map for Fractal Structures in Weak Interactions of Solitary Waves

2008/02/25 by Yi Zhu, Richard Haberman, Jianke Yang · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Elasticity and Wave Propagation #Nonlinear Dynamics and Pattern Formation #nlin.CD #nlin.PS

paper · pdf · doi:10.1103/physrevlett.100.143901

4 pages, 3 figures to appear in Phys. Rev. Lett. (2008)

arxiv created 2008/02/25 · openalex publication_date 2008/04/10 · arxiv updated 2012/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations

Cited by

• Separatrix Map Analysis for Fractal Scatterings in Weak Interactions of Solitary Waves
• Radiationless energy exchange in three-soliton collisions

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