Solutions of Analytical Systems of Partial Differential Equations

TL;DR

This paper investigates classes of linear and nonlinear analytical PDE systems, deriving integrability conditions and providing solutions as functional series near a specific point, enhancing understanding of their solvability.

Contribution

It identifies integrability conditions for general PDE systems and offers a method to construct solutions as functional series when conditions are met.

Findings

Integrability conditions for PDE systems are established.

Solutions can be expressed as functional series near a point.

Provides a framework for solving certain classes of PDEs.

Abstract

In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x=0).