Titlebook: Nonlinear PDE’s in Condensed Matter and Reactive Flows; Henri Berestycki,Yves Pomeau Book 2002 Springer Science+Business Media Dordrecht 2

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1389-2185 such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.978-1-4020-0973-0978-94-010-0307-0Series ISSN 1389-2185

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Symmetric Vortex Solutions in the ,(1) and ,(5) Ginzburg-Landau Models of Superconductivitype of vortex profile with antiferromagnetic ordering in the core region. In the process we revisit the traditional .(1)-Ginzburg-Landau vortices and prove the uniqueness of symmetric solutions of degree . for κ ≥ |.|√2.

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On Some Reaction-Diffusion Systems with Nonlinear Diffusion Arising in Biologydness of the parabolic problems, .∞ bounds on the solutions which do not depend on time and a study of their large time behavior; it turns out that the solution pairs converge to constants as . tends to infinity. However their transient behavior may be very complex and phenomena such as tip splitting may occur at intermediate times.

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Spirals in Excitable Mediaspirals and of their counterparts, retracting waves, from this viewpoint, in the free boundary limit where the propagating excited region is bounded by a sharp interface. Spiral drift in an imposed electric field is also described as an example of application of the analysis.

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