SYMMETRIES OF THE VARIABLE-COEFFICIENT KDV EQUATION AND 3 HIERARCHIES OF THE INTEGRODIFFERENTIAL VARIABLE-COEFFICIENT KDV EQUATION

By using a simple method to factorize the recurison 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 tau symmetries. Starting from these sets of symmetries, we obtained three hierarchies of the variable coefficient KdV integro-differential equations.