| 概要 | We define the Schroedinger equation with focusing, cubic nonlinearity on a star graph. We study the dynamics of a solitary wave in the high velocity regime. We show that after colliding with the vertex a soliton splits in reflected and transmitted components. Over a time scale of logarithmic order in the velocity, the mass spreads over the edges of the graph according to the reflection and transmission coefficients associated to the linear problem. Over the same time scale, the outgoing waves preserve a soliton character. In the analysis we follow ideas borrowed from the seminal paper about scattering of fast solitons by a delta interaction on the line, by Holmer, Marzuola and Zworski; our work represents an extension of their results to the case of graphs and, as a byproduct, it shows how to extend their analysis to the scattering of solitons by more singular point interactions on the line.
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