Abstract
We survey applications of the Hamiltonian approach and group theory to ideal fluid dynamics and integrable systems. In particular, we review the derivations of the Landau-Lifschitz and Korteweg-de Vries equations as Euler equations on certain infinite-dimensional groups.
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Khesin, B. (2009). The Group and Hamiltonian Descriptions of Hydrodynamical Systems. In: Ricca, R. (eds) Lectures on Topological Fluid Mechanics. Lecture Notes in Mathematics(), vol 1973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00837-5_4
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DOI: https://doi.org/10.1007/978-3-642-00837-5_4
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