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 …
Lie group formalism for difference equations
The methods of Lie group analysis of differential equations are generalized so as to provide
an infinitesimal formalism for calculating symmetries of difference equations. Several …
an infinitesimal formalism for calculating symmetries of difference equations. Several …
[图书][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 …
Symmetries of discrete dynamical systems
D Levi, P Winternitz - Journal of Mathematical Physics, 1996 - pubs.aip.org
The purpose of this article is to classify differential–difference equations (DE) of the form n
ün t Fn t, un 1 t, un t, un 1 t 0, 1.1 into conjugacy classes and to determine the Lie point …
ün t Fn t, un 1 t, un t, un 1 t 0, 1.1 into conjugacy classes and to determine the Lie point …
Small-amplitude envelope solitons in nonlinear lattices
VV Konotop - Physical Review E, 1996 - APS
The general theory of small-amplitude envelope solitons in one-dimensional lattices with
cubic and quartic nonlinearities is developed. It is shown for a wide diversity of interactions …
cubic and quartic nonlinearities is developed. It is shown for a wide diversity of interactions …
Bright compact breathers
PG Kevrekidis, VV Konotop - Physical Review E, 2002 - APS
In this communication we will consider the potential of some general classes of nonlinear
lattice models to support bright discrete compact breather solutions (compactlets). We …
lattice models to support bright discrete compact breather solutions (compactlets). We …
Symmetries of discrete dynamical systems involving two species
D Gomez-Ullate, S Lafortune, P Winternitz - arXiv preprint solv-int …, 1998 - arxiv.org
The Lie point symmetries of a coupled system of two nonlinear differential-difference
equations are investigated. It is shown that in special cases the symmetry group can be …
equations are investigated. It is shown that in special cases the symmetry group can be …
Lattice-solitons in radiation damage
FM Russell, DR Collins - Nuclear Instruments and Methods in Physics …, 1995 - Elsevier
Energetic lattice-solitons are created during radiation damage processes and transport
energy through the lattice until scattered by major defects or are dispersed by lateral …
energy through the lattice until scattered by major defects or are dispersed by lateral …
A highly accurate numerical method for solving nonlinear time‐fractional differential difference equation
This work is based on the implementation of an iterative perturbation method to attain the
series solutions of nonlinear fractional differential difference equation (NFDΔE). Perturbation …
series solutions of nonlinear fractional differential difference equation (NFDΔE). Perturbation …
Symmetry classification of diatomic molecular chains
S Lafortune, S Tremblay, P Winternitz - arXiv preprint nlin/0204021, 2002 - arxiv.org
A symmetry classification of possible interactions in a diatomic molecular chain is provided.
For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant …
For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant …