Inserted: 26 oct 2005
Last Updated: 3 dec 2005
Journal: Duke Math. J.
In this paper we describe a natural framework for the vortex dynamics in the parabolic complex Ginzburg-Landau equation in $R^2$. This general setting does not rely on any assumption of well-preparedness and has the advantage to be valid even after collision times. We analyze carefully collisions leading to annihilation. A new phenomenon is identified, the phase-vortex interaction, related to persistence of low frequency oscillations, and leading to an unexpected drift in the motion of vortices.
2000 Mathematics Subject Classification : 35B40, 35K55, 35Q40.
Keywords: parabolic equations, Ginzburg-Landau, vortex dynamics