Continuous symmetries of difference equations

D Levi, P Winternitz - Journal of Physics A: Mathematical and …, 2005‏ - iopscience.iop.org
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 …

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 …

Direct linearization of nonlinear difference-difference equations

FW Nijhoff, GRW Quispel, HW Capel - Physics Letters A, 1983‏ - Elsevier
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 …

Linear integral equations and nonlinear difference-difference equations

GRW Quispel, FW Nijhoff, HW Capel… - Physica A: Statistical …, 1984‏ - Elsevier
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 …

Nonlinear differential difference equations as Backlund transformations

D Levi - Journal of Physics A: Mathematical and General, 1981‏ - iopscience.iop.org
Shows that the best known nonlinear differential difference equations associated with the
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 …

[PDF][PDF] Conditions for the existence of higher symmetries of evolutionary equations on the lattice

D Levi, R Yamilov - Journal of Mathematical Physics, 1997‏ - matem.anrb.ru
Nonlinear differential-difference equations are always more important in applications. They
enter as models for many biological chains, are encountered frequently in queuing problems …

The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula

G Wang, QP Liu, H Mao - Journal of Physics A: Mathematical and …, 2020‏ - iopscience.iop.org
This paper is concerned with the modified Camassa–Holm equation and its Bäcklund
transformation. With the aid of reciprocal transformation and the associated modified …

Transformations of quadrilateral lattices

A Doliwa, PM Santini, M Manas - Journal of Mathematical Physics, 2000‏ - pubs.aip.org
Motivated by the classical studies on transformations of conjugate nets, we develop the
general geometric theory of transformations of their discrete analogs: the multidimensional …

Integrable dynamics of a discrete curve and the Ablowitz–Ladik hierarchy

A Doliwa, PM Santini - Journal of Mathematical Physics, 1995‏ - pubs.aip.org
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 …