INTEGRABLE QUARTIC POTENTIALS AND COUPLED KDV EQUATIONS

We show a surprising connection between known integrable Hamiltonian s ystems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the 1:6:1 integrable case quartic potential. A generalisation of the 1:6:8 case is similarly related to a different ( but gauge related) fourth order Lax operator We exploit this connectio n to derive a Lax representation for each of these integrable systems. In this context, a canonical transformation is derived through a gaug e transformation.