Dresden 2017 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 32: Quantum Chaos
DY 32.9: Talk
Wednesday, March 22, 2017, 12:30–12:45, HÜL 186
Stationary waves on nonlinear quantum graphs: Canonical perturbation theory — •Daniel Waltner1 and Sven Gnutzmann2 — 1Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg — 2School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
We present a general framework for solving the stationary nonlinear Schrödinger equation on a network of one-dimensional wires modelled by a metric graph with suitable matching conditions at the vertices. For sufficiently small intensities we use canonical perturbation theory that allows to reproduce characteristic effects of nonlinear equations like bifurcations and multistabilities. Simple closed and scattering graphs serve as examples.