Symmetries, Associated First Integrals, and Double Reduction of Difference Equations
نویسندگان
چکیده
منابع مشابه
First Integrals/Invariants & Symmetries for Autonomous Difference Equations
For the autonomous kth order difference equation xn+k = f(xn, xn+1, . . . , xn+k−1), where f ∈ C[U ] with domain U ⊂ R, a global first integral/invariant for this difference equation is a nonconstant function H ∈ C[U ], with H : U → R, which remains invariant on the forward orbit Γ(x0, x1, . . . , xk−1). If a first integral exists, then it satisfies a particular functional difference equation a...
متن کاملHidden Symmetries, First Integrals and Reduction of Order of Nonlinear Ordinary Differential Equations
The reduction of nonlinear ordinary differential equations by a combination of first integrals and Lie group symmetries is investigated. The retention, loss or even gain in symmetries in the integration of a nonlinear ordinary differential equation to a first integral are studied for several examples. The differential equations and first integrals are expressed in terms of the invariants of Lie...
متن کاملReduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کاملFeynman integrals and difference equations
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ∗-fields. We test the implementaion of the Mathematica package Sigma on examples from recent higher order perturbati...
متن کاملContinuous 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 more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalize...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2014
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2014/490165