A 3-component extension of the Camassa-Holm hierarchy
Laura Fontanelli, Paolo Lorenzoni, Marco Pedroni
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.
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