Dressing the Dressing Chain
Copyright policy )Dressing the Dressing Chain
The dressing chain is derived by applying Darboux transformations to the spectral problem of the Korteweg-de Vries (KdV) equation. It is also an auto-Bäcklund transformation for the modified KdV equation. We show that by applying Darboux transformations to the spectral problem of the dressing chain one obtains the lattice KdV equation as the dressing chain of the dressing chain and, that the lattice KdV equation also arises as an auto- Bäcklund transformation for a modified dressing chain. In analogy to the results obtained for the dressing chain (Veselov and Shabat proved complete integrability for odd dimensional periodic reductions), we study the (0; n)-periodic reduction of the lattice KdV equation, which is a two-valued correspondence. We provide explicit formulas for its branches and establish complete integrability for odd n.
- La Trobe University Australia
- Shanghai University China (People's Republic of)
discrete dressing chain, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Liouville integrability, lattice KdV, Pure mathematics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Mathematical sciences, Partial difference equations, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Applied mathematics, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, Darboux transformations, KdV equations (Korteweg-de Vries equations), FOS: Mathematics, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Mathematical Physics
discrete dressing chain, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Liouville integrability, lattice KdV, Pure mathematics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Mathematical sciences, Partial difference equations, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Applied mathematics, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, Darboux transformations, KdV equations (Korteweg-de Vries equations), FOS: Mathematics, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Mathematical Physics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!