Proof of the Completeness of Darboux Wronskian Formulae for Order Two
Analysis of PDEs
2013-04-24 v5 Mathematical Physics
Differential Geometry
math.MP
Abstract
Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one cannot be represented this way. It has been a long standing problem on what are other exceptions. In our previous work we proved that among transformations of total order one there are no other exceptions. Here we prove that for transformations of total order two there are no exceptions at all. We also obtain a simple explicit invariant description of all possible Darboux Transformations of total order two.
Keywords
Cite
@article{arxiv.1111.1338,
title = {Proof of the Completeness of Darboux Wronskian Formulae for Order Two},
author = {Ekaterina Shemyakova},
journal= {arXiv preprint arXiv:1111.1338},
year = {2013}
}