Vanishing waves on closed intervals and propagating short-range phenomena.
Variation of a nonlinear temperature field connected with the coefficient of heat conductivity.
Variation of constants formula for functional parabolic partial differential equations.
Viscous profiles of vortex patches
Vortex rings for the Gross-Pitaevskii equation
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension . 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 ).