Darboux transformations for linear operators on two dimensional regular lattices

Details Darboux transformations for linear operators on two dimensional regular lattices Darboux transformations for linear operators on two dimensional regular lattices

2009-05-21

arxiv.org/abs/0905.3484v2

J. Phys. A: Math. Theor. 42 (2009) 454001

Nonlinear Sciences

Exactly Solvable and Integrable Systems

23 pages, 3 figures, presentation improved

Scientific paper

10.1088/1751-8113/42/45/454001

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.

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