Darboux transformations for a 6-point scheme

Details Darboux transformations for a 6-point scheme Darboux transformations for a 6-point scheme

2006-06-08

arxiv.org/abs/nlin/0606025v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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.

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