Results 41 to 50 of about 2,243,156 (179)

Quantization scheme for modular q-difference equations [PDF]

, 2004
Modular pairs of some second order q-difference equations are considered. These equations may be interpreted as a quantum mechanics of a sort of hyperelliptic pendulum.
Sergeev, S.
core   +2 more sources

New class of practically solvable systems of difference equations of hyperbolic-cotangent-type

Electronic Journal of Qualitative Theory of Differential Equations, 2020
The systems of difference equations $$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$,
Stevo Stevic
doaj   +1 more source

Differential-difference equations reducible to difference and q-difference equations

Computers & Mathematics with Applications, 2001
Asymptotic properties of solutions of the differential-difference equation \[ x'(qt+1)=h(x(t))x'(t), \quad t\geq 0,\;q\geq 1 \tag{*} \] are investigated. Let \(\varphi\in C^1([0,1];\mathbf R)\) satisfies \(\varphi'(1)=h(\varphi(0))\varphi'(0)\). A solution \(x\) of (*) satisfying \(x(t)=\varphi(t)\), \(t\in [0,1)\), is denoted by \(x_{\varphi}\).
openaire   +1 more source

Invariant manifolds for analytic difference equations

, 2012
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference equations do not ...
de la Llave, Rafael, Lomeli, Hector E.
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Classification of five-point differential-difference equations

, 2016
Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations.
Garifullin, R. N., Levi, D., Yamilov, R. I.   +2 more
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Advances in Difference Equations

Axioms
This editorial concerns the Special Issue of Axioms entitled “Advances in Difference Equations” [...]
Azhar Ali Zafar
doaj   +1 more source

On oscillatory solutions of certain difference equations [PDF]

Opuscula Mathematica, 2006
Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
Grzegorz Grzegorczyk, Jarosław Werbowski   +1 more
doaj  

Difference systems in bond and face variables and non-potential versions of discrete integrable systems

, 2017
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively.
Kassotakis, Pavlos, Nieszporski, Maciej
core   +1 more source

On difference equations with ‘B’-type solitons on three dimensional lattice

Partial Differential Equations in Applied Mathematics
In this paper we discuss an example of classical integrable equation with rather unusual ‘B’-type Kadomtsev–Petviashvili (KP) soliton hierarchy.
Sergey M. Sergeev
doaj   +1 more source

Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations

Advances in Difference Equations, 2018
We represent general solution to a homogeneous linear difference equation of second order in terms of a specially chosen solution to the equation and apply it to get a representation of general solution to the bilinear difference equation in terms of a ...
Stevo Stević
doaj   +1 more source