Vortices and Factorization

Igor Loutsenko, Oksana Yermolayeva

Published 2024-03-12Version 1

We review applications of factorization methods to the problem of finding stationary point vortex patterns in two-dimensional fluid mechanics. Then we present a new class of patterns related to periodic analogs of Schrodinger operators from the ``even" bi-spectral family. We also show that patterns related to rational and soliton solutions of the KdV hierarchy constitute complete solution of the problem for certain classes of vortex systems.