PDE seminar Nonlinear Schroedinger equation on star graphs: scattering of fast

2011-1-12 17:00 - 2011-1-12 18:00
Faculty of Science Building #3 Room 309
Claudio Cacciapuoti (University of Bonn/Tohoku University)
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 the
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.
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.

* Please note change in date, start time, place this week