Nonlinear Schrodinger Equations

Wednesday, November 2, 2016 - 11:30am - 12:20pm
Dmitry Pelinovsky (McMaster University)
Standing waves in the focusing nonlinear Schrodinger (NLS) equation are considered on a dumbbell graph (two rings attached to a central line segment subject to the Kirchhoff boundary conditions at the junctions). In the small-norm limit, the ground state (the orbitally stable standing wave of the smallest energy at a fixed $L^2$ norm) is represented by a constant solution.
Tuesday, November 1, 2016 - 11:30am - 12:20pm
Christof Sparber (University of Illinois, Chicago)
The possibility of finite-time, dispersive blow up for nonlinear equations of Schrödinger type is revisited. We extend earlier results in the literature to include the multi-dimensional case, as well as the case of Davey-Stewartson and Gross-Pitaevskii equations. As a by-product of our analysis, a sharp global smoothing estimate for the integral term appearing in Duhamel’s formula is obtained.
Monday, October 31, 2016 - 3:15pm - 4:05pm
Panayotis Kevrekidis (University of Massachusetts)
Motivated by work in nonlinear optics, as well as more recently
in Bose-Einstein condensate mixtures, we will explore a
series of nonlinear states that arise in such systems. We
will start from a single structure, the so-called dark-bright solitary wave, and then
expand our considerations to multiple such waves, their
spectral properties, nonlinear interactions and experimental
observations. A twist will be to consider the dark
solitons of the one component as effective potentials that will trap the bright
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