Darboux transformations for a 6-point scheme

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.

Cited by in corpus (2)

• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• Darboux transformations for linear operators on two dimensional regular lattices