Far East Journal of Dynamical Systems
Volume 14, Issue 1, Pages 1 - 15
(September 2010)
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NOTES ON KHESIN-MISIOŁEK METRICS ON THE VIRASORO ALGEBRA
Keiichi Kikuchi
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Abstract:
We consider the completion of the Virasoro algebra with Khesin-Misiołek metrics via Sobolev spaces and adjoint operators of certain linear operators. From the Euler equation on the completion of the Virasoro algebra, we are lead to the transformation equation of motion and obtain some shallow water-type equations which contain the Khesin-Misiołek’s equation. |
| Keywords and phrases: Euler equation, Virasoro algebra, Shallow water equation. |
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