Non-Laplacian growth: Exact results

We study integrable generalizations of the Laplacian growth, describing flows in inhomogeneous porous media. The boundary is driven by a field satisfying an elliptic PDE, that is not generally reduced to a Beltrami–Laplace equation (“Non-Laplacian” growth). These turn out to be PDEs of the Calogero–Moser type, related to finite reflection groups as well as their integrable deformations.