A three-parameter difference Hamiltonian operator, corresponding pair of Hamiltonian operators and a family of Liouville integrable lattice equations. (English) Zbl 1221.37154
Summary: A difference Hamiltonian operator involved three arbitrary real parameters is introduced. When these parameters in the difference Hamiltonian operator are properly chosen, we obtain a pair of difference Hamiltonian operators. Then, using Magri’s scheme of bi-Hamiltonian formulation, we construct a family of Liouville integrable lattice equations. Finally, the discrete zero curvature representation of obtained family is presented.
MSC:
| 37K60 | Lattice dynamics; integrable lattice equations |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 39A70 | Difference operators |
Keywords:
difference Hamiltonian operator; bi-Hamiltonian formulation; integrable lattice equation; Liouville integrable; discrete zero curvature representationReferences:
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