New Applications of Quantum Algebraically Integrable Systems in Fluid Dynamics
Exactly Solvable and Integrable Systems
2019-02-26 v2 Mathematical Physics
Analysis of PDEs
math.MP
Fluid Dynamics
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.
Cite
@article{arxiv.1211.2906,
title = {New Applications of Quantum Algebraically Integrable Systems in Fluid Dynamics},
author = {Anne Boutet de Monvel and Igor Loutsenko and Oksana Yermolayeva},
journal= {arXiv preprint arXiv:1211.2906},
year = {2019}
}