Universal map for fractal structures in weak interactions of solitary waves

Fractal scatterings in weak solitary-wave interactions are analyzed for generalized nonlinear Schr?diger 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.