Laplace transformations as the only degenerate Darboux transformations of first order

@article{Shemyakova2012LaplaceTA,
  title={Laplace transformations as the only degenerate Darboux transformations of first order},
  author={Ekaterina Shemyakova},
  journal={Programming and Computer Software},
  year={2012},
  volume={38},
  pages={105-108}
}
The paper is devoted to the Darboux transformations, an effective algorithm for finding analytical solutions of partial differential equations. It is proved that Wronskian-like formulas suggested by G. Darboux for the second-order linear operators on the plane describe all possible differential transformations with M of the form D x + m(x, y) and D y + m(x, y), except for the Laplace transformations. 

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Laplace ’ s Cascade Integration Method for Linear Hyperbolic Systems of Equations

  • S. Ya. Startsev
  • 2008

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