Inverse problem of group analysis for autonomous differential systems

TL;DR

This paper constructs a comprehensive set of autonomous, solvable differential systems using Lie group theory, infinitesimal operators, and invariants, advancing the understanding of their structure and solutions.

Contribution

It introduces a method to build all autonomous solvable differential systems based on Lie group invariants and structure constants, expanding the theoretical framework.

Findings

Complete set of solvable differential systems constructed

Utilizes Lie group invariants and structure constants

Applicable to abelian and non-abelian groups

Abstract

Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and non-abelian).