Vortices and Factorization
Abstract
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 soliton solutions of the KdV hierarchy constitute complete solution of the problem for certain classes of vortex systems. Keywords: Point vortices in ideal fluid, Factorization of second- and third-order differential operators, KdV and Sawada-Kotera hierarchies, Bispectral problem, Locus configurations
Cite
@article{arxiv.2403.07537,
title = {Vortices and Factorization},
author = {Igor Loutsenko and Oksana Yermolayeva},
journal= {arXiv preprint arXiv:2403.07537},
year = {2025}
}
Comments
Two sections and an appendix have been added to the initial manuscript. The appendix has been slightly extended compared to the corresponding article in Reviews in Mathematical Physics