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arXiv · 2403.07537

Vortices and Factorization

Igor Loutsenko·Oksana Yermolayeva
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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

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Igor Loutsenko, Oksana Yermolayeva. 2024-03-12. Vortices and Factorization. https://doi.org/10.1142/s0129055x2530002x

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