Symmetries of the Variable Coefficient KdV Equation and ThreeHierarchies of the Integrodifferential Variable Coefficient KdV Equation

By using a simple method to factorize the recursion operator, the inverse recursion operator of the variable coefficient KdV cquqtion is exhibited explicitly. Thee new sets of symmetries of the variable coefficient KdV equation arc given in addition to the known K symmetries and τ symmetries. Starting from these three sets of symmetries, we obtained three hierarchies of the variable coefficient KdV integro-differential equations.