Darboux transformations for a 6-point scheme
Exactly Solvable and Integrable Systems
2015-06-26 v1 Differential Geometry
Abstract
We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate to solving a hyperbolic type initial-boundary value problem. We discuss several reductions and specifications of the transformations as well as construction of other Darboux covariant schemes by means of existing ones. In particular we introduce a 10-point scheme which can be regarded as the discretization of self-adjoint hyperbolic equation.
Cite
@article{arxiv.nlin/0606025,
title = {Darboux transformations for a 6-point scheme},
author = {Maciej Nieszporski},
journal= {arXiv preprint arXiv:nlin/0606025},
year = {2015}
}