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TMF, 2019, Volume 199, Number 2, Pages 175–192 (Mi tmf9607)  

This article is cited in 1 scientific paper (total in 1 paper)

Factorization of Darboux–Laplace transformations for discrete hyperbolic operators

S. V. Smirnov

Department of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We classify elementary Darboux–Laplace transformations for semidiscrete and discrete second-order hyperbolic operators. We prove that there are two types of elementary Darboux–Laplace transformations in the $($semi$)$discrete case as in the continuous case: Darboux transformations constructed from a particular element in the kernel of the initial hyperbolic operator and classical Laplace transformations that are defined by the operator itself and are independent of the choice of an element in the kernel. We prove that on the level of equivalence classes in the discrete case, any Darboux–Laplace transformation is a composition of elementary transformations.

Keywords: Darboux–Laplace transformation, discrete hyperbolic operator, factorization.

Funding Agency Grant Number
Russian Science Foundation 16-11-10260
This research was done at Lomonosov Moscow State University and was supported by a grant from the Russian Science Foundation (Project No. 16-11-10260).


DOI: https://doi.org/10.4213/tmf9607

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English version:
Theoretical and Mathematical Physics, 2019, 199:2, 621–636

Bibliographic databases:

Received: 26.07.2018
Revised: 27.09.2018

Citation: S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, TMF, 199:2 (2019), 175–192; Theoret. and Math. Phys., 199:2 (2019), 621–636

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Cheng Zhang, Linyu Peng, Da-jun Zhang, “Discrete Crum's theorems and lattice KdV-type equations”, Theoret. and Math. Phys., 202:2 (2020), 165–182  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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