Abstract

We show a surprising connection between known integrable Hamiltonian systems 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 connection to derive a Lax representation for each of these integrable systems. In this context, a canonical transformation is derived through a gauge transformation.

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