Bicomplexes and Bäcklund transformations

2001/04/30 by Aristophanes Dimakis, A Dimakis, Folkert Muller-Hoissen +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Mathematics and Applications #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/0305-4470/34/43/306

published as J.Phys.A34:9163-9194,2001 · Substantially revised version with several additions, 38 pages, to appear in J. Phys. A

arxiv created 2001/09/27 · openalex publication_date 2001/10/19 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

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 Bäcklund transformations for several models. The method also works for Moyal-deformed equations with a corresponding deformed bicomplex.

Citations

• Bicomplexes and integrable models

Cited by

• Non-commutative Ward's conjecture and integrable systems
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2 + 1 dimensions
• Towards noncommutative integrable systems