Frontiers in Nonlinear Waves in honor of Vladimir Zakharov's 70th birthday. Noncommutative vortices and beach waves. G. Cruz L.R. Juárez A. A. Minzoni M. Rosenbaum. IIMAS-FENOMEC, UNAM. Pelinovsky, Kevrekidis, Frantzeskikis 2005. Circular vortex. Peierls-Nabarro potential. Static vortex.
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Frontiers in Nonlinear Wavesin honor of Vladimir Zakharov's 70th birthday
Noncommutative vortices and beach waves
A. A. Minzoni
Pelinovsky, Kevrekidis, Frantzeskikis 2005
Noncommutative NLS equation
The last expression is the equation of motion for the peak of the vortex, analogous to a particle in a Peierls-Nabarro potential.
Large vortex with low energy
The vortex moves in the lattice generated by the *-product.
The fixed points are the equilibrium positions