This article is cited in 4 papers

Two-sided Darboux transformations

A. B. Shabat^ab, Z. S. El'kanova^a, A. B. Urusova<sup>a

a</sup> Aliev Karachaev--Cherkess State University, Karachaevsk, Russia
^b Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

Abstract: We refine the notion of a Darboux transformation for differential operators of an order higher than two and consider commutative rings of differential operators that are invariant under the group of dilations of the independent variable.

Keywords: Darboux transformation, commutative ring of differential operators, third-order Bessel equation.

Received: 04.05.2012

DOI: 10.4213/tmf8356

 English version: Theoretical and Mathematical Physics, 2012, 173:2, 1507–1517

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