Mathematics Colloquia and Seminars

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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.