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arXiv · math-ph/0601066

Non-Laplacian growth, algebraic domains and finite reflection groups

Igor Loutsenko·Oksana Yermolayeva
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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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Igor Loutsenko, Oksana Yermolayeva. 2006-02-26. Non-Laplacian growth, algebraic domains and finite reflection groups. https://doi.org/10.1063/1.2204809

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