Time-dependent recursion operators and symmetries

The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed hat he symmetries of he integrable evolution equations obtained through heir recursion operators do not satisfy the symmetry equations. There have been several attempts to resolve his problem. It is shown that in the case of time-dependent evolution equations or time-dependent recursion operators associativity is lost. Due to this fact such recursion operators need modi cation. A general formula is given for he missing term of the recursion operators. Apart from he recursion operators a method is introduced to calculate the correct symmetries. For illustrations several examples of scalar and coupled system of equations are considered.