Proof of the Completeness of Darboux Wronskian Formulae for Order Two
Printed: Jun 2013
Darboux Wronskian formulas allow to construct Darboux transformations,
but Laplace transformations, which are Darboux transformations of
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.
completeness of Darboux Wronskian formulas, completeness of Darboux determinants, Darboux transformations, invariants for solution of PDEs
53Z05 - Applications to physics
35Q99 - None of the above, but in this section