Complete integrability of Lagrangian mappings and lattices of KdV type

We present the Lagrangian and (time-discrete) Hamiltonian structures of lattice discretizations of the KdV equation, as well as of the associated finite-dimensional mappings that we derived earlier. Complete integrability in the sense of Liouville of these mappings is established by showing involuti...

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Bibliographic Details
Published in:Physics letters. A 1991-05, Vol.155 (6), p.377-387
Main Authors: Capel, H.W., Nijhoff, F.W., Papageorgiou, V.G.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Physics
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Summary:We present the Lagrangian and (time-discrete) Hamiltonian structures of lattice discretizations of the KdV equation, as well as of the associated finite-dimensional mappings that we derived earlier. Complete integrability in the sense of Liouville of these mappings is established by showing involutivity of a complete set of integrals of the discrete-time dynamics. Similar results hold for lattices and mappings related to the MKdV and Toda equations.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(91)91043-D