Invariants for systems of two linear hyperbolic-type equations by complex methods

TL;DR

This paper explores invariants of a specific subclass of linear hyperbolic PDE systems using complex and real methods, revealing that complex methods can identify unique invariants not found by traditional real symmetry analysis.

Contribution

It introduces a complex method approach to find invariants of hyperbolic PDE systems, showing that this approach uncovers additional invariants compared to real methods.

Findings

Complex invariants differ from real invariants.

Complex methods reveal new invariants.

Comparison shows the effectiveness of complex approach.

Abstract

Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general system of linear hyperbolic PDEs is investigated for the associated invariants, by complex as well as real methods. The complex procedure relies on the correspondence of systems of PDEs with the base complex equation. Complex invariants of the base complex PDEs are shown to reveal invariants of the corresponding systems. A comparison of all the invariant quantities obtained by complex and real methods for this class, is presented which shows that the complex procedure provides a few invariants different from those extracted by real symmetry analysis.