Generalized Euler-Poincar, Equations on Lie Groups and Homogeneous Spaces, Orbit Invariants and Applications

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-Poincar, 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-Poincar, equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, mu CH and mu DP equations, and the geodesic equations with respect to right-invariant Sobolev metrics on the group of diffeomorphisms of the circle.


Published in:
Letters In Mathematical Physics, 97, 45-60
Year:
2011
Publisher:
Springer Verlag
ISSN:
0377-9017
Keywords:
Laboratories:




 Record created 2011-12-16, last modified 2018-01-28


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