New Applications of Quantum Algebraically Integrable Systems in 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.

References in corpus (3)

• Equilibrium of charges and differential equations solved by polynomials
• The Variable Coefficient Hele-Shaw Problem, Integrability and Quadrature Identities
• Integrable Dynamics of Charges Related to Bilinear Hypergeometric Equation

Cited by in corpus (1)

• On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth