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Fractal scatterings in weak solitary wave interactions is analyzed forgeneralized nonlinear Schr\"odiger equations (GNLS). Using asymptotic methods,these weak interactions are reduced to a universal second-order map. This mapgives the same fractal scattering patterns as those in the GNLS equations bothqualitatively and quantitatively. Scaling laws of these fractals are alsoderived.

A Universal Map for Fractal Structures in Weak Solitary Wave Interactions