Bäcklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations

Friedemann Brandt

doi:10.1063/1.530517

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arXiv · hep-th/9405064

Bäcklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations

Friedemann Brandt

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Abstract

It is shown that Bäcklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.

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Friedemann Brandt. 1994-05-10. Bäcklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations. https://doi.org/10.1063/1.530517

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