# Some Algebraically Solvable Two-Dimensional Dynamical Systems with Polynomial Interactions

## TL;DR

This paper reviews a technique for identifying algebraically solvable two-dimensional nonlinear ODE systems with polynomial interactions, and presents new specific examples of such systems with complex variables.

## Contribution

It introduces new examples of algebraically solvable polynomial two-dimensional ODE systems, expanding the class of known solvable models.

## Key findings

- Examples of polynomial 2D ODE systems solvable by algebraic operations.
- Extension of previously reported systems with new specific cases.
- Potential applications in modeling complex dynamical phenomena.

## Abstract

We tersely review a recently introduced technique to identify systems of two nonlinearly-coupled Ordinary Di{\S}erential Equations (ODEs) solvable by algebraic operations; and we report some specifc examples of this kind, namely systems of 2 first-order ODEs with polynomial right-hand sides, x_ n= P(n)(x1, x2) , n = 1, 2 , satisfied by the 2 (possibly complex ) dependent variables xn = xn (t). Here P(n)(x1, x2) indicates some specific polynomial. These examples are analogous, but different, from those previously reported.