Symmetries of the Variable Coefficient KdV Equation and Three Hierarchies of the Integro differential Variable Coefficient KdV Equation

Abstract

By using a simple method to factorize the recursion operator, the inverse recursion operator of the variable coefficient KdV equation is exhibited explicitly. Three new sets of symmetries of the variable coefficient KdV equation are 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.