prof. Noja's seminar at SISSA

Emanuele Tuillier Illingworth tuillier at
Thu May 8 13:25:48 CEST 2014


prof Diego Noja (Univ. di Milano Bicocca)

TITLE: The Nonlinear Schroedinger equation with point interactions: 
localized defects and concentrated nonlinearities

Short summary:

The nonlinear Schroedinger equation (NLSE) is a model for several
physical phenomena, the most known of which are wave propagation in a
nonlinear optical medium and dynamics of Bose Einstein condensates. It
is also a mathematical paradigm for the interplay between dispersion and 
nonlinearity in Hamiltonian PDEs.
In this talk will be considered some models of NLSE with space dependent
coefficients represented by zero range interactions. Zero range
coefficients appear in NLSE in two ways. The first one is a point defect 
acting as an external potential, for example a delta or delta prime 
interaction; so the linear part of the NLSE as a Schroedinger operator 
turns out to be a point interaction. The second way is a spatially 
inhomogeneous nonlinearity, ideally concentrated at a point.
An introduction to these models and to the more recent results and open
problems will be given, with an emphasis on stability properties of
standing waves.

Venue: Thursday 22 May at 4 pm in lecture room 005

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