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arXiv · 1008.4377

Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications

Feride Tiglay·Cornelia Vizman
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Abstract

We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincaré equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincaré equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, $μ$CH and $μ$DP equations, and the geodesic equations with respect to right invariant Sobolev metrics on the group of diffeomorphisms of the circle.

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Feride Tiglay, Cornelia Vizman. 2010-08-25. Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications. https://doi.org/10.1007/s11005-011-0464-2

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