Darboux transformations for a 6-point scheme
Maciej Nieszporski
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.
Create a lesson
Related papers
Sato-theoretic construction of the anti-self-dual Yang-Mills hierarchy and the Ward conjecture
Shangshuai Li, Da-jun Zhang
Direct linearization, Cauchy matrix and Sato Grassmannian
Kanehisa Takasaki
The transformations of the mToda hierarchy in tau functions
Wenchuang Guan, Shen Wang, Bailin Zhang et al.
Multiparameter Quantum Affine Spaces and the Scalene Yang--Baxter Equation
Pramod Padmanabhan, Somnath Maity, Vladimir Korepin
Long-time asymptotics of the integrable defocusing Wadati-Konno-Ichikawa equation with a finite-genus algebro-geometric background
Taohua Luo, Zhenya Yan, Guoqiang Zhang
New 5th-order Schwarzian evolution equations and their higher-order symmetries
Marianna Euler, Norbert Euler