Recursion Operators for a Class of Integrable Third-Order Evolution Equations

We consider   u_t = u ^α u_xxx + n ( u ) u_xu_xx + m ( u ) u ³ _x + r ( u ) u_xx + p ( u ) u ² _x + q ( u ) u_x + 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.