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Continuous symmetries of difference equations
Lie group theory was originally created more than 100 years ago as a tool for solving
ordinary and partial differential equations. In this article we review the results of a much …
ordinary and partial differential equations. In this article we review the results of a much …
Bäcklund transformation, exact solutions and interaction behaviour of the (3+ 1)-dimensional Hirota-Satsuma-Ito-like equation
SJ Chen, WX Ma, X Lü - … in Nonlinear Science and Numerical Simulation, 2020 - Elsevier
Abstract In this paper, a (3+ 1)-dimensional Hirota-Satsuma-Ito-like equation is introduced
based on the (2+ 1)-dimensional Hirota-Satsuma-Ito equation. Bäcklund transformation and …
based on the (2+ 1)-dimensional Hirota-Satsuma-Ito equation. Bäcklund transformation and …
Direct linearization of nonlinear difference-difference equations
Starting from the linear integral equation for the solutions of the Korteweg-de Vries (KdV)
equation, we obtain the direct linearization of a general nonlinear difference-difference …
equation, we obtain the direct linearization of a general nonlinear difference-difference …
Linear integral equations and nonlinear difference-difference equations
In this paper we present a systematic method to obtain various integrable nonlinear
difference-difference equations and the associated linear integral equations from which their …
difference-difference equations and the associated linear integral equations from which their …
Nonlinear differential difference equations as Backlund transformations
Shows that the best known nonlinear differential difference equations associated with the
discrete Schrodinger spectral problem and also with the discrete Zakharov-Shabat spectral …
discrete Schrodinger spectral problem and also with the discrete Zakharov-Shabat spectral …
[كتاب][B] Continuous symmetries and integrability of discrete equations
D Levi, P Winternitz, RI Yamilov - 2023 - books.google.com
This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …
symmetries and integrability techniques to the case of equations defined on the lattice. This …
[PDF][PDF] Conditions for the existence of higher symmetries of evolutionary equations on the lattice
Nonlinear differential-difference equations are always more important in applications. They
enter as models for many biological chains, are encountered frequently in queuing problems …
enter as models for many biological chains, are encountered frequently in queuing problems …
The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula
This paper is concerned with the modified Camassa–Holm equation and its Bäcklund
transformation. With the aid of reciprocal transformation and the associated modified …
transformation. With the aid of reciprocal transformation and the associated modified …
Transformations of quadrilateral lattices
Motivated by the classical studies on transformations of conjugate nets, we develop the
general geometric theory of transformations of their discrete analogs: the multidimensional …
general geometric theory of transformations of their discrete analogs: the multidimensional …
Integrable dynamics of a discrete curve and the Ablowitz–Ladik hierarchy
It is shown that the following elementary geometric properties of the motion of a discrete (ie,
piecewise linear) curve select the integrable dynamics of the Ablowitz–Ladik hierarchy of …
piecewise linear) curve select the integrable dynamics of the Ablowitz–Ladik hierarchy of …