Darboux transformations for linear operators on two dimensional regular lattices

Abstract

Darboux transformations for linear operators on regular two dimensional lattices are reviewed. The six point scheme is considered as the master linear problem, whose various specifications, reductions, and their sublattice combinations lead to other linear operators together with the corresponding Darboux transformations. The second part of the review deals with multidimensional aspects of (basic reductions of) the four point scheme, as well as the three point scheme.

23 pages, 3 figures, presentation improved

References in corpus (6)

• Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
• The B-quadrilateral lattice, its transformations and the algebro-geometric construction
• Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
• Integrable dynamics of Toda-type on the square and triangular lattices
• On $\tau$-function of the quadrilateral lattice
• Darboux transformations for a 6-point scheme

Cited by in corpus (4)

• Discrete KP equation with self-consistent sources
• Discrete Darboux system with self-consistent sources and its symmetric reduction
• Factorization of Darboux-Laplace transformations for discrete hyperbolic operatros
• Bäcklund transformations as integrable discretization. The geometric approach