Connection between the infinite sequence of Lie-Backlund symmetries of the Korteweg-de Vries and sine-Gordon equations

From the observation that the infinite sequence of Lie-Backlund symmetries of the potential modified Kortweg-deVries (PMK-dV) and the sine-Gordon (s-G) equations are identical, it is shown that there exists a simple connection between the Lie-Backlund symmetries (written in the form of evolution equations) of the Korteweg-deVries (K-dV) and s-G equations. Further, this connection is similar to the one obtained by Chodos for the conserved quantities of K-dV and s-G equations. We also point out that the result of Chodos can be realized from the equality of conserved densities of PMK-dV and s-G systems