Backlund Transformations for Darboux Integrable Differential Systems: Examples and Applications
Differential Geometry
2015-09-03 v2
Abstract
In the article arXiv:1108.5443 we established a general group-theoretical approach to the construction of B\"acklund transformations. We then showed how this construction can be applied to construct B\"acklund transformation between equations which are Darboux integrable. Here we give a number of detailed examples and new applications which demonstrate the theory. In particular our final example demonstrates how our group theoretical approach produces all the B\"acklund transformations in arXiv:0707.4408. We also prove, using group methods, a non-existence theorem for B\"acklund transformatons which disagrees with part 2 of Theorem 1 in arXiv:0707.4408.
Cite
@article{arxiv.1407.3011,
title = {Backlund Transformations for Darboux Integrable Differential Systems: Examples and Applications},
author = {Ian M. Anderson and Mark E. Fels},
journal= {arXiv preprint arXiv:1407.3011},
year = {2015}
}
Comments
This is a substantial rewrite of v1 with more details provided in the examples