Non-Laplacian growth, algebraic domains and finite reflection groups

Details Non-Laplacian growth, algebraic domains and finite reflection groups Non-Laplacian growth, algebraic domains and finite reflection groups

2006-01-31

arxiv.org/abs/math-ph/0601066v3

J.Math.Phys. 47 (2006) 062702

Physics

Mathematical Physics

Scientific paper

10.1063/1.2204809

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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