Integrable Quartic Potentials and Coupled KdV Equations

S. Baker; V. Z. Enolskii; A. P. Fordy

doi:10.1016/0375-9601(95)00267-7

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arXiv · hep-th/9504087

Integrable Quartic Potentials and Coupled KdV Equations

S. Baker·V. Z. Enolskii·A. P. Fordy

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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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S. Baker, V. Z. Enolskii, A. P. Fordy. 1995-04-18. Integrable Quartic Potentials and Coupled KdV Equations. https://doi.org/10.1016/0375-9601(95)00267-7

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