# Journal of Nonlinear Mathematical Physics

Volume 26, Issue 4, July 2019, Pages 509 - 519

# Two Peculiar Classes of Solvable Systems Featuring 2 Dependent Variables Evolving in Discrete-Time via 2 Nonlinearly-Coupled First-Order Recursion Relations

Authors
Francesco Calogeroa, b, *, , Farrin Payandehc, , §
aPhysics Department, University of Rome “La Sapienza”, Rome, Italy
bINFN, Sezione di Roma 1
cDepartment of Physics, Payame Noor University, PO BOX 19395-3697 Tehran, Iran
Corresponding Authors
Francesco Calogero, Farrin Payandeh
Received 13 March 2019, Accepted 6 April 2019, Available Online 9 July 2019.
DOI
10.1080/14029251.2019.1640460How to use a DOI?
Abstract

In this paper we identify certain peculiar systems of 2 discrete-time evolution equations,

x˜n=F(n)(x1,x2),n=1,2,
which are algebraically solvable. Here is the “discrete-time” independent variable taking integer values ( = 0, 1, 2,...), xnxn() are 2 dependent variables, and x˜nxn(+1) are the corresponding 2 updated variables. In a previous paper the 2 functions F(n)(x1,x2), n = 1, 2, were defined as follows: F(n)(x1,x2) = P2 (xn,xn+1), n = 1,2 mod[2], with P2(x1,x2) a specific second-degree homogeneous polynomial in the 2 (indistinguishable!) dependent variables x1() and x2(). In the present paper we further clarify some aspects of that model and we present its extension to the case when F(n)(x1,x2)=Qk(n)(x1,x2), n = 1, 2, with Qk(n)(x1,x2) a specific homogeneous function of arbitrary (integer) degree k (hence a polynomial of degree k when k > 0) in the 2 dependent variables x1() and x2().

Open Access

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
26 - 4
Pages
509 - 519
Publication Date
2019/07/09
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2019.1640460How to use a DOI?
Open Access

TY  - JOUR
AU  - Francesco Calogero
AU  - Farrin Payandeh
PY  - 2019
DA  - 2019/07/09
TI  - Two Peculiar Classes of Solvable Systems Featuring 2 Dependent Variables Evolving in Discrete-Time via 2 Nonlinearly-Coupled First-Order Recursion Relations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 509
EP  - 519
VL  - 26
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1640460
DO  - 10.1080/14029251.2019.1640460
ID  - Calogero2019
ER  -