A new family of integrable differential systems in arbitrary dimension

TL;DR

This paper introduces a broad class of differential systems in any dimension that are either integrable or completely integrable, expanding known families and providing numerous examples across various systems.

Contribution

It presents a new, extensive family of integrable differential systems applicable in arbitrary dimensions, including many classical and complex examples.

Findings

Includes new integrable systems in various dimensions.

Extends known families of planar integrable systems.

Provides numerous illustrative examples.

Abstract

We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that illustrates the applicability of our approach. For instance, in the plane this list includes some Li\'enard, Lotka--Volterra and quadratic systems; in the space, some Kolmogorov, Rikitake and R\"ossler systems. Examples of complete integrable systems in higher dimensions are also provided.