Backlund Transformations for Darboux Integrable Differential Systems

Details Backlund Transformations for Darboux Integrable Differential Systems Backlund Transformations for Darboux Integrable Differential Systems

2011-08-27

arxiv.org/abs/1108.5443v1

Mathematics

Differential Geometry

72 pages

Scientific paper

We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund transformation can be constructed by the proposed symmetry reduction method. It is then shown that the well-known Backlund transformations between Darboux integrable Monge-Ampere systems can all be constructed using group quotients. A simple group theoretical argument leads to a non-existence result for Backlund transformations which disagrees with Theorem 1 in arXiv:0707.4408v2. A variety of examples are given.

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