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Petr Plechac, Vladimir Sverak:

On self-similar singular solutions of the complex Ginzburg-Landau equation.

We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigourous results and numerical computations, we describe a countable family of self-similar singularities. Our analysis includes the super-critical non-linear Schr\"odinger equation as a special case. We also consider the problem of stability of these singularities.

 Bibliographical note: Comm. Pure and Appl. Mathematics, 54 (2001), 1215-1242 










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