Factorization of Darboux-Laplace transformations for discrete hyperbolic operatros
arXiv:1811.04506 · doi:10.4213/tmf9607
Abstract
Elementary Darboux--Laplace transformations for semidiscrete and discrete second order hyperbolic operators are classified. It is proved that in the (semi)-discrete case there are two types of elementary Darboux--Laplace transformations as well: Darboux transformations that are defined by the choice of particular element in the kernel of the initial hyperbolic operator and classical Laplace transformations that are defined by the operator itself. It is proved that in the discrete case on the level of equivalence classes any Darboux--Laplace transformation is a product of elementary ones.
16 pages
References in corpus (5)
- On Darboux integrability of discrete 2D Toda lattices
- Classification of Multidimensional Darboux Transformations: First Order and Continued Type
- Differential operators on the superline, Berezinians, and Darboux transformations
- Darboux transformations for differential operators on the superline
- Discrete Crum's Theorems and Integrable Lattice Equations