Displaying similar documents to “Vortices in Ginzburg-Landau equations.”

Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part II: The dynamics

Sylvia Serfaty (2007)

Journal of the European Mathematical Society

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We deduce from the first part of this paper [S1] estimates on the energy-dissipation rates for solutions of the Ginzburg–Landau heat flow, which allow us to study various phenomena occurring in this flow, including vortex collisions; they allow in particular extending the dynamical law of vortices past collision times.

On the Ginzburg-Landau and related equations

Yu N. Ovchinnikov, Israel Michael Sigal (1997-1998)

Séminaire Équations aux dérivées partielles

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We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture...