Math Colloquium:
Wednesday, April 12, 2023
3:00 PM-4:00 PM
Abstract:
I will overview generalizations of the nonlinear Schrodinger equation, where either the spatially decaying (solitary) waves are singular due to cusped singularities or the time evolution near solitary waves is singular. Both classes of models correspond to realms of nonlinear optics with intensity-dependent dispersion. For the models of the former class, I will show how weak formulations and ODE theory can be used to prove stability of solitary waves under perturbations which do not change the length between nearest singularities. For the models of the latter class, I will show how the energy, mass, and momentum conservation can be used to control perturbations in weighted Sobolev spaces
Contact Information
Darij Grinberg
dg899@drexel.edu