Singularity Formation in Nonlinear Schrodinger Equations with Fourth-Order Dispersion
Wednesday, October 27, 2004 - 1:30pm - 2:20pm
Boaz Ilan (University of Colorado)
Similarly to the classical NLS, NLS equations with fourth-order dispersion can admit singularity formation. Such equations arise in the studies of optical-beam propagation in fiber arrays and in the numerical analysis of finite-difference discretizations of the NLS. We extend the classical-NLS global-existence theory to the NLS with isotropic and anisotropic fourth-order dispersion. Using the results on the critical exponent, it is shown how fourth-order dispersion can assist in the physical realization of spatio-temporal light bullets in a pure Kerr medium. These are recent works with Gadi Fibich, George Papanicolaou, Steve Schochet, and Shimshon Bar-Ad.