New Applications of Quantum Algebraically Integrable Systems in Fluid Dynamics

TL;DR

This paper explores the extension of quantum algebraically integrable systems to fluid dynamics, specifically viscous free-boundary flows in non-homogeneous media, introducing new solutions and methods for higher dimensions.

Contribution

It introduces a novel connection between algebraically integrable systems and fluid flow problems, extending solutions beyond conformal mapping techniques to higher dimensions.

Findings

Extended Laplacian growth models to non-homogeneous media.

Constructed solutions using Adler-Moser polynomials.

Developed methods for higher-dimensional fluid flows.

Abstract

The rational quantum algebraically integrable systems are non-trivial generalizations of Laplacian operators to the case of elliptic operators with variable coefficients. We study corresponding extensions of Laplacian growth connected with algebraically integrable systems, describing viscous free-boundary flows in non-homogenous media. We introduce a class of planar flows related with application of Adler-Moser polynomials and construct solutions for higher-dimensional cases, where the conformal mapping technique is unavailable.