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

Download Citation

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

Vol.64 • No. 1 • April 2020
Back to Top