Integrability of invariant metrics on the diffeomorphism group of the circle

• Autores: Adrian Constantin, B. Kolev
• Localización: Journal of nonlinear science, ISSN 0938-8974, Vol. 16, Nº 2, 2006, págs. 109-122
• Idioma: inglés
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• Resumen

  • Each Hk Sobolev inner product (k ? 0) defines a Hamiltonian vector field Xk on the regular dual of the Lie algebra of the diffeomorphism group of the circle. We show that only X0 and X1 are bi-Hamiltonian relative to a modified Lie-Poisson structure.