Integrability of reductions of the discrete Korteweg–de Vries and potential Korteweg–de Vries equations
Copyright policy )Integrability of reductions of the discrete Korteweg–de Vries and potential Korteweg–de Vries equations
We study the integrability of mappings obtained as reductions of the discrete Korteweg–de Vries (KdV) equation and of two copies of the discrete potential KdV (pKdV) equation. We show that the mappings corresponding to the discrete KdV equation, which can be derived from the latter, are completely integrable in the Liouville–Arnold sense. The mappings associated with two copies of the pKdV equation are also shown to be integrable.
- UNSW Sydney Australia
- University of Kent United Kingdom
- La Trobe University Australia
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Pure mathematics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Mathematical sciences, FOS: Physical sciences, Partial difference equations, integrable maps, partial difference equations, Physical sciences, Symplectic mappings, fixed points (dynamical systems), Poisson brackets, Engineering, Lattice dynamics; integrable lattice equations, Hamiltonian structures, symmetries, variational principles, conservation laws
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Pure mathematics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Mathematical sciences, FOS: Physical sciences, Partial difference equations, integrable maps, partial difference equations, Physical sciences, Symplectic mappings, fixed points (dynamical systems), Poisson brackets, Engineering, Lattice dynamics; integrable lattice equations, Hamiltonian structures, symmetries, variational principles, conservation laws
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