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math.SG2020★ 29 cited
Geometric hydrodynamics and infinite-dimensional Newton's equations
Boris Khesin, Gerard Misiolek, Klas Modin
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability dens…
math.SG2002★ 2 cited
Euler equations on homogeneous spaces and Virasoro orbits
B. Khesin, G. Misiolek
We show that the following three systems related to various hydrodynamical approximations: the Korteweg--de Vries equation, the Camassa--Holm equation, and the Hunter--Saxton equat…