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The evolution equations mentioned in the title of this paper read as follows:x~n = P(n)(x1; x2) , n = 1, 2 , where l is the "discrete-time" independentvariable taking integer values (l =0, 1, 2, ...), xn = xn (l) are the 2dependent variables, x~n = xn (l + 1), and the 2 functions P(n)(x1, x2), n = 1,2, are 2 polynomials in the 2 dependent variables x1 (l) and x2 (l). Theresults reported in this paper have been obtained by an appropriatemodification of a recently introduced technique to obtain analogous results incontinuous-time t in which case xn = xn (t) and the above recursion relationsare replaced by first-order ODEs. Their potential interest is due to therelevance of this kind of evolution equations in various applicative contexts.

journal of nonlinear mathematical physics

Solvable Systems Featuring 2 Dependent Variables Evolving in  Discrete-Time via 2 Nonlinearly-Coupled First-Order Recursion Relations with  Polynomial Right-Hand Sides