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April 2020 Classification of Darboux transformations for operators of the form xy+ax+by+c
Ekaterina Shemyakova
Illinois J. Math. 64(1): 71-92 (April 2020). DOI: 10.1215/00192082-8165598

Abstract

Darboux transformations are nongroup-type symmetries of linear differential operators. One can define Darboux transformations algebraically by the intertwining relation ML=L1M or the intertwining relation ML=L1N in the cases when the former is too restrictive.

Here we show that Darboux transformations for operators of the form L=xy+ax+by+c (sometimes referred to as 2D Schrödinger operators or Laplace operators) are always compositions of atomic Darboux transformations of two different well-studied types of Darboux transformations, provided that the chain of Laplace transformations for the original operator is long enough.

Citation

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Ekaterina Shemyakova. "Classification of Darboux transformations for operators of the form xy+ax+by+c." Illinois J. Math. 64 (1) 71 - 92, April 2020. https://doi.org/10.1215/00192082-8165598

Information

Received: 22 January 2019; Revised: 1 November 2019; Published: April 2020
First available in Project Euclid: 6 March 2020

zbMATH: 07179190
MathSciNet: MR4072642
Digital Object Identifier: 10.1215/00192082-8165598

Subjects:
Primary: 16S32
Secondary: 37K25 , 37K35

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 1 • April 2020
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