On solvability of a two-dimensional symmetric nonlinear system of difference equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-27 DOI:10.1186/s13660-024-03186-2

Stevo Stević, Bratislav Iričanin, Witold Kosmala, Zdeněk Šmarda

引用次数: 0

Abstract

We show that the system of difference equations $$ x_{n+k}=\frac{x_{n+l}y_{n}-ef}{x_{n+l}+y_{n}-e-f},\quad y_{n+k}= \frac{y_{n+l}x_{n}-ef}{y_{n+l}+x_{n}-e-f},\quad n\in {\mathbb{N}}_{0}, $$ where $k\in {\mathbb{N}}$ , $l\in {\mathbb{N}}_{0}$ , $l< k$ , $e, f\in {\mathbb{C}}$ , and $x_{j}, y_{j}\in {\mathbb{C}}$ , $j=\overline{0,k-1}$ , is theoretically solvable and present some cases of the system when the general solutions can be found in a closed form.

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论二维对称非线性差分方程组的可解性

我们证明了差分方程组 $$ x_{n+k}=\frac{x_{n+l}y_{n}-ef}{x_{n+l}+y_{n}-e-f}、\quad y_{n+k}= \frac{y_{n+l}x_{n}-ef}{y_{n+l}+x_{n}-e-f},\quad n\in {\mathbb{N}}_{0}, $$ 其中 $k\in {\mathbb{N}}$ 、其中 $k\in {\mathbb{N}}$ , $l\in {\mathbb{N}}_{0}$ , $l< k$ , $e, f\in {\mathbb{C}}$ , $x_{j}, y_{j}\in {\mathbb{C}}$ , $j=\overline{0,k-1}$ 在理论上是可解的，并给出了系统的一些情况，即一般解可以以封闭形式求得。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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