Symmetric nonlinear solvable system of difference equations
We show the theoretical solvability of the system of difference equations $$x_{n+k}=\frac{y_{n+l}y_n-cd}{y_{n+l}+y_n-c-d},\quad y_{n+k}=\frac{x_{n+l}x_n-cd}{x_{n+l}+x_n-c-d},\quad n\in\mathbb{N}_0,$$ where $k\in\mathbb{N}$, $l\in\mathbb{N}_0$, $l<k$, $c, d\in\mathbb{C}$ and $x_j, y_j\in\mathbb{C}...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2024-09-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11195 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We show the theoretical solvability of the system of difference equations
$$x_{n+k}=\frac{y_{n+l}y_n-cd}{y_{n+l}+y_n-c-d},\quad y_{n+k}=\frac{x_{n+l}x_n-cd}{x_{n+l}+x_n-c-d},\quad n\in\mathbb{N}_0,$$
where $k\in\mathbb{N}$, $l\in\mathbb{N}_0$, $l<k$, $c, d\in\mathbb{C}$ and $x_j, y_j\in\mathbb{C}$, $j=\overline{0,k-1}$. For several special cases of the system, we give some detailed explanations on how some formulas for their general solutions can be found in closed form, that is, we show their practical solvability. To do this, among other things, we use the theory of homogeneous linear difference equations with constant coefficients and the product-type difference equations with integer exponents, which are theoretically solvable. |
|---|---|
| ISSN: | 1417-3875 |