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Nonlinear Schrodinger equation on star-graphs
Fri 08 February 2013, 14:00
Claudio Cacciapuoti
Hausdorff Center for Mathematics, Bonn
Organiser: Nina Snaith
ABSTRACT
A metric graph is a metric space which can be written as the union of compact or non compact intervals (the "edges" of the graph). A simple example of metric graph is the star-graph, which is the union of N halflines with common origin (the "vertex" of the graph). It is known that one can define PDEs on graphs. On a star-graph, a PDE is equivalently written as a system of N equations on the positive real axis coupled by suitable gluing conditions in the origin. In this talk I will discuss several properties of the nonlinear Schrodinger equation on a star-graph in the case of focusing nonlinearity of power type. I will give explicit formulae for the stationary states and I will discuss existence and stability of the ground state, defined as the minimizer of the constrained action functional.