Linearisation of Universal Field Equations

TL;DR

This paper demonstrates that the Universal Field Equations can be linearized through a Legendre transformation, supporting their classification as integrable systems, and provides explicit solutions for a broad class of cases.

Contribution

It shows the linearization of Universal Field Equations via Legendre transformation, confirming their integrability and offering explicit solutions for many instances.

Findings

Universal Field Equations are linearizable by Legendre transformation.

The equations are confirmed to be integrable systems.

Explicit solutions are obtainable for a large class of solutions.

Abstract

The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the conjecture that these equations describe integrable systems. While this construction is implicit in general, there exists a large class of solutions for which an explicit form may be written.