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Self-focusing and singularity formation in the nonlinear Schrodinger equation
Probability| Speaker: | Gadi Fibich, Tel Aviv University |
| Location: | 693 Kerr |
| Start time: | Tue, Feb 1 2000, 1:10PM |
Description
The formation of singularities in the critical nonlinear Schrodinger
equation (NLS) has been used to predict that sufficiently intense
laser beams can undergo catastrophic self-focusing. In the first part
of this talk I will present some recent results on conditions for
singularity formation in the NLS on bounded and unbounded domains. In
the second part of this talk I will show that when weak vectorial
effects(which come from the vectorial nature of Maxwell's equations)
are included in the model, singularity formation is arrested. In
addition, vectorial effects can explain the phenomena of multiple-
filamentation, i.e. breakup of an axially-symmetric input beam
into several long and narrow filaments.