B\"acklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations
High Energy Physics - Theory
2009-10-28 v1 Analysis of PDEs
Abstract
It is shown that B\"acklund 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.
Keywords
Cite
@article{arxiv.hep-th/9405064,
title = {B\"acklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations},
author = {Friedemann Brandt},
journal= {arXiv preprint arXiv:hep-th/9405064},
year = {2009}
}
Comments
25 pages