On the decoupling problem of general quasilinear first order systems in two independent variables

TL;DR

This paper investigates the decoupling problem for general quasilinear first order systems in two variables, providing conditions based on eigenvalues and eigenvectors for partial or full decoupling, with applications in physics.

Contribution

It offers necessary and sufficient conditions for decoupling such systems, including differential constraints and transformation methods, applicable to various physical models.

Findings

Conditions for decoupling depend on eigenvalues and eigenvectors.

Differential constraints enable decoupling transformations.

Applications include physically relevant systems.

Abstract

The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous systems. Necessary and sufficient conditions for the partial or full decoupling of the systems at hand are provided. The conditions involve the properties of eigenvalues and eigenvectors of the coefficient matrix, and provide the differential constraints whose integration leads to the decoupling transformation. Some applications of physical interest are also given.