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Colloquium
Thursday, March 13, 2014


Singularities in natural systems -- existence and stability

Vivi Rottschaefer (Leiden)


Abstract: In this talk we study the formation of singularities in natural systems. Singularities arise when nonlinear effects dominate the dispersive ones, up to the formation of the singularity. We focus on projects that are motivated by concrete applications. As a model problem, we study the complex Ginzburg-Landau equation in the limit of small dissipation so that it can be viewed as a small perturbation of the nonlinear Schroedinger equation. For this equation, multi-bump, blowup,self-similar solutions are found by combining numerical, asymptotical and geometrical methods. So far, the stability of these blowup solutions had only been examined numerically. We use Evans function techniques developed for perturbations of Hamiltonian systems to study the stability of the ring-type solutions that were found depending on the parameters in the system.

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Location :  Room 611 of the Hans Freudenthal building, formerly known as the Wiskunde/Maths building, (campus De Uithof) Budapestlaan 6, Utrecht.
Date and time : Thursday, March 13, 2014 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.