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Laplace transformations as the only degenerate Darboux transformations of first order

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Abstract

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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  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    Ekaterina Shemyakova

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  1. Ekaterina Shemyakova
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Correspondence to Ekaterina Shemyakova.

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Original Russian Text © Ekaterina Shemyakova, 2012, published in Programmirovanie, 2012, Vol. 38, No. 2.

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Shemyakova, E. Laplace transformations as the only degenerate Darboux transformations of first order. Program Comput Soft 38, 105–108 (2012). https://doi.org/10.1134/S0361768812020053

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  • DOI: https://doi.org/10.1134/S0361768812020053

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