Recursion operators for a class of integrable third-order evolution equations

We consider ut=uuxxx+n(u)uxuxx+m(u)u3x+r(u)uxx+p(u)u2x+q(u)ux+s(u) with α= 0 and α= 3, for those functional forms of m, n, p, q, r, s for which the equation is integrable in the sense of an infinite number of Lie–Bäcklund symmetries. Recursion operators which are x- and t-independent that generate these infinite sets of (local) symmetries are obtained for the equations. A combination of potential forms, hodograph transformations, and x-generalized hodograph transformations are applied to the obtained equations.Validerad; 2004; 20061005 (evan