Symmetric nonlinear solvable system of difference equations

We show the theoretical solvability of the system of difference equations x n + k = y n + l y n − c d y n + l + y n − c − d , y n + k = x n + l x n − c d x n + l + x n − c − d , n ∈ N 0 , where k ∈ N , l ∈ N 0 , l < k , c , d ∈ C and x j , y j ∈ C , j = 0 , k − 1 ¯ . For several special cases of...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2024-01, Vol.2024 (49), p.1-16
Main Authors: Stević, Stevo, Iricanin, Bratislav, Kosmala, Witold
Format: Article
Language:English
Subjects:
solution in closed form
solvable system
symmetric system of difference equations
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Summary:We show the theoretical solvability of the system of difference equations x n + k = y n + l y n − c d y n + l + y n − c − d , y n + k = x n + l x n − c d x n + l + x n − c − d , n ∈ N 0 , where k ∈ N , l ∈ N 0 , l < k , c , d ∈ C and x j , y j ∈ C , j = 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
1417-3875
DOI:10.14232/ejqtde.2024.1.49