First integrals of linear differential systems

TL;DR

This paper develops a spectral method to construct a basis of first integrals for multidimensional and ordinary linear differential systems with constant coefficients, aiding in their analysis and solution.

Contribution

It introduces a novel spectral approach for finding first integrals in linear differential systems with constant coefficients, expanding existing methods.

Findings

Spectral method successfully constructs first integrals basis.

Method applicable to multidimensional and ordinary systems.

Enhances understanding of linear differential systems' integrability.

Abstract

We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of linear differential equations is developed.