  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.
