Proof of the Completeness of Darboux Wronskian Formulae for Order Two

Details Proof of the Completeness of Darboux Wronskian Formulae for Order Two Proof of the Completeness of Darboux Wronskian Formulae for Order Two

2011-11-05

arxiv.org/abs/1111.1338v4

Mathematics

Analysis of PDEs

Scientific paper

Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations 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.

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