Abstract
In the present paper, we identify the integrability of thethird-order nonlinear evolution equation ut = (1/2)({({uxx+u})−2})x in a Hamiltonian viewpoint. We prove thatthe recursion operator obtained by S.Yu. Sakovich is hereditary, and thendeduce a bi-Hamiltonian structure of the equation by using somedecomposition of the hereditary operator. A hierarchy associated to theequation is also shown.
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