Inserted: 6 jun 2003
Last Updated: 20 feb 2004
Journal: J. Eur. Math. Soc.
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross-Pitaevskii (GP) equation in dimension $N\ge 3.$ We also extend the asymptotic analysis of the free field Ginzburg-Landau equation to a larger class of equations, including the Ginzburg-Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if $N=3$).
Keywords: Non linear Schroedinger equation, travelling waves, prescribed curvature equation