Preprint GA 10/2003

On two recent generalizations of the Harry Dym equation

By S. Yu. Sakovich

Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy, are transformed into previously known integrable systems: one-into a pair of decoupled KdV equations, the other one-into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.