We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl (2) endowed with a suitable Poisson pair. It gives rise to the usual Camassa-Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation
Fontanelli, L., Lorenzoni, P., Pedroni, M. (2006). A three-component extension of the Camassa-Holm hierarchy. LETTERS IN MATHEMATICAL PHYSICS, 78(2), 125-137 [10.1007/s11005-006-0109-z].
A three-component extension of the Camassa-Holm hierarchy
LORENZONI, PAOLO;
2006
Abstract
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl (2) endowed with a suitable Poisson pair. It gives rise to the usual Camassa-Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation
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