Integrable quartic potentials and coupled KdV equations

Baker, S.; Enolsky, V.Z.; Fordy, A.P.

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

Integrable quartic potentials and coupled KdV equations

S. Baker
(
- Leeds U.
)
,
V.Z. Enolsky
(
- Kiev, Inst. Metal Phys.
)
,
A.P. Fordy
(
- Leeds U.
)

Apr, 1995

11 pages

Published in:

Phys.Lett.A 201 (1995) 167

e-Print:

hep-th/9504087 [hep-th]

DOI:

10.1016/0375-9601(95)00267-7

Report number:

ETM-95-04

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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.

References(4)

Figures(0)

ON THE INTEGRABILITY OF A SYSTEM OF COUPLED KDV EQUATIONS

R. Dodd
(
- Trinity Coll., Dublin
)
,
A. Fordy
(
- Manchester U.
)

- Phys.Lett.A 89 (1982) 168-170
•
DOI:
- 10.1016/0375-9601(82)90199-2

Linear r matrix algebra for systems separable in parabolic coordinates

J.C. Eilbeck
(
- Heriot-Watt U.
)
,
V.Z. Enolsky
(
- Heriot-Watt U. and
- Kiev, Inst. Metal Phys.
)
,
V.B. Kuznetsov
(
- Amsterdam U.
)
,
D.V. Leykin
(
- Kiev, Inst. Metal Phys.
)

- Phys.Lett.A 180 (1993) 208
•
e-Print:
- hep-th/9308143
•
DOI:
- 10.1016/0375-9601(93)90697-X

- Physica D 52 201

- Phys.Lett.A 191 91