A 3-component extension of the Camassa-Holm hierarchy
arXiv:nlin/0604040 · doi:10.1007/s11005-006-0109-z
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 CH hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a 3-component extension of the CH equation.
15 pages; minor changes; to appear in Letters in Mathematical Physics