The Darboux-type transformations of integrable lattices.

DOI10.1016/S0034-4877(01)80064-1zbMath1078.37518WikidataQ104434213 ScholiaQ104434213MaRDI QIDQ696312

Adam Doliwa

Publication date: 12 September 2002

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Riemann surfacesDarboux transformationsintegrable lattices

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Projective differential geometry (53A20) Lattice dynamics; integrable lattice equations (37K60)

Related Items (2)

New hierarchies of integrable lattice equations and associated properties: Darboux transformation, conservation laws and integrable coupling ⋮ N-fold Darboux transformation and soliton solutions for Toda lattice equation

Cites Work

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• \(\bar \partial\)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice
• Quadratic reductions of quadrilateral lattices
• The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice
• Darboux transformations for multidimensional quadrilateral lattices. I
• Multidimensional quadrilateral lattices are integrable.
• Geometric discretisation of the Toda system.
• Transformations of quadrilateral lattices
• Charged free fermions, vertex operators and the classical theory of conjugate nets
• Three–dimensional integrable lattices in Euclidean spaces: conjugacy and orthogonality
• Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method

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