ON THE NONHEREDITARY RECURSION OPERATOR AND THE CONSTRAINT ON THE POTENTIAL ASSOCIATED WITH THE GIACHETTI-JOHNSON EQUATION AND ITS GAUGE EQUIVALENT YANG EQUATION

The recursion operator associated with the Giachetti-Johnson (GJ) equation is shown not to be hereditary. Restricting the potential to the invariant subspace of the recursion operator leads to a constraint on the potential. Under the constraint two systems obtained from the GJ equation and the related time evolution equation for eigenfunctions are shown to be naturally consistent. Constants of the motion for former system are given and a solution to this system satisfies a certain higher-order stationary equation. Also, similar results are obtained for the Yang equation.