Theoretical and Mathematical Physics

, Volume 189, Issue 3, pp 1681–1692 | Cite as

Bäcklund transformations



We describe a Bäcklund transformation, i.e., a differentially related pair of differential equations, in a coordinate manner appropriate for calculations and applications. We present several known explanatory examples, including Bäcklund transformations for gauge fields in a Minkowski space of arbitrary dimension.


total derivative partial differential equation differential relation constraint Bäcklund transformation gauge field curvature tensor covariant derivative Yang–Mills field 


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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Mathematical Institute of Russian Academy of SciencesMoscowRussia

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