A Universal Map for Fractal Structures in Weak Solitary Wave Interactions

TL;DR

This paper derives a universal second-order map that captures fractal scattering patterns in weak solitary wave interactions across generalized nonlinear Schrödinger equations, revealing scaling laws and unifying diverse fractal behaviors.

Contribution

It introduces a universal map that accurately models fractal scattering in weak solitary wave interactions for GNLS equations, providing a unified analytical framework.

Findings

The universal map reproduces fractal scattering patterns both qualitatively and quantitatively.

Scaling laws for the fractals are derived from the map.

The approach applies broadly to generalized nonlinear Schrödinger equations.

Abstract

Fractal scatterings in weak solitary wave interactions is analyzed for generalized nonlinear Schr\"odiger 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.