Event № 243
This is joint work with Daniel Waltner (Duisburg-Essen)building on previous work with Uzy Smilansky (Weizmann Institute) andStanislav Derevyanko (now Ben Gurion University).I will consider solutions to the stationary nonlinearSchrödinger equation on a metric graph with `standard' matchning conditions.I will summarise the framework and show how the coupled differentialequations reduce to a finite number of algebraic nonlinear equations.In the low intensity limit these equations reduce to well-know linearequations for (linear) quantum graphs. A particularly interesting limitis te short wavelength limit as it allows for a regime with locally weaknonlinearity but strong global effects. These effects can be captured inthe leading order in a canonical Hamiltonian perturbation theory. Somesimple examples will be discussed.If time allows I will present a few open questions that are currentlybeing investigated with Ram Band and August Krueger here at the Technion.