Bicomplexes and Backlund transformations

Details Bicomplexes and Backlund transformations Bicomplexes and Backlund transformations

2001-04-30

arxiv.org/abs/nlin/0104071v2

J.Phys.A34:9163-9194,2001

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Substantially revised version with several additions, 38 pages, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/34/43/306

A bicomplex is a simple mathematical structure, in particular associated with completely integrable models. The conditions defining a bicomplex are a special form of a parameter-dependent zero curvature condition. We generalize the concept of a Darboux matrix to bicomplexes and use it to derive Backlund transformations for several models. The method also works for Moyal-deformed equations with a corresponding deformed bicomplex.

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