A Universal Map for Fractal Structures in Weak Solitary Wave Interactions

来源 :International Conference Nonlinear Waves-Theory and Applicat | 被引量 : 0次 | 上传用户:l444715055
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  It is known that solitary wave interactions exhibit fractal scatterings in non-integrable systems.This phenomenon has been reported and studied in various physical systems.Most of these studies focused on strong interactions, i.e.collisions.In this talk, fractal scatterings in weak solitary wave interactions is analyzed for the generalized nonlinear Schr(o)dinger equations.with arbitrary nonlinearities.Using the Karpman-solovev pertur bation method, the dynamics of these interactions is first reduced to a universal twodegree-of-freedom Hamiltonian ODE system.Then using asymptotic methods along the separatrix orbits of the reduced ODEs, a simple but universal second-order map is derived.Comparison with direct PDE and ODE computations confirms that the map completely captures all major aspects of fractal scatterings in the PDEs and their reduced ODEs, and the maps prediction is asymptotically accurate.The criterion for the existence of fractal scatterings and the scaling laws of these fractals are also derived analytically from the analysis of the map.
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