Differential Invariants and Hidden Symmetry

TL;DR

This paper explores classes of PDEs with hidden symmetries, revealing how their reduced forms exhibit additional symmetries, especially under Lorentz and Euclidean transformations, and discusses their relation to conditional symmetry and equivalence classes.

Contribution

It introduces new classes of PDEs with hidden and conditional symmetries and analyzes their relation to symmetry groups and equation equivalence.

Findings

Identification of PDE classes with hidden symmetries under rotations and boosts

Analysis of the relation between hidden, conditional symmetry, and equation equivalence

Discussion of symmetry properties in Lorentz and Euclidean groups

Abstract

We describe some classes of PDE that display hidden symmetry, with reduced equations having additional symmetry operators compared to the initial equations. Relations between the concepts of hidden and conditional symmetry, and between hidden symmetry and equivalence of classes of equations, is discussed. In particular, we describe equations having hidden and conditional symmetry under rotations and boosts in the Lorentz and Euclid groups.