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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Noncommutative vortices and beach waves
A. A. Minzoni
The last expression is the equation of motion for the peak of the vortex, analogous to a particle in a Peierls-Nabarro potential.
The vortex moves in the lattice generated by the *-product.
The fixed points are the equilibrium positions