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Invertible Darboux transformations of type I. (English. Russian original) Zbl 1406.44003
Program. Comput. Softw. 41, No. 2, 119-125 (2015); translation from Programmirovanie 41, No. 2 (2015).
Summary: In the paper, a general category-based approach to invertible Darboux transformations is suggested. For operators of arbitrary dimension and arbitrary order, it is suggested to consider Darboux transformations of certain type, namely, of type I. Explicit compact formulas are obtained. In particular, any invertible Darboux transformations of first order and, for example, Laplace transformations are type I transformations. For operators of third order in the plane, analogues of the Darboux transformation chains are obtained.

##### MSC:
 44A15 Special integral transforms (Legendre, Hilbert, etc.) 35A30 Geometric theory, characteristics, transformations in context of PDEs
LPDO
Full Text:
##### References:
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