Non-Laplacian growth, algebraic domains and finite reflection groups
arXiv:math-ph/0601066 · doi:10.1063/1.2204809
Abstract
Dynamics of planar domains with moving boundaries driven by the gradient of a scalar field that satisfies an elliptic PDE is studied. We consider the question: For which kind of PDEs the domains are algebraic, provided the field has singularities at a fixed point inside the domain? The construction reveals a direct connection with the theory of the Calogero-Moser systems related to finite reflection groups and their integrable deformations.
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