New Symmetry Groups for Generalized Solutions of ODEs

TL;DR

This paper demonstrates that simple ordinary differential equations possess numerous additional symmetry groups when their generalized solutions are analyzed within a specialized algebraic framework, expanding the understanding of their symmetry properties.

Contribution

It introduces new symmetry groups for ODEs by considering generalized solutions in a differential algebra, extending classical symmetry analysis.

Findings

Existence of many new symmetry groups for simple ODEs

Generalized solutions reveal symmetries not seen in classical analysis

Expands the theoretical framework for symmetry analysis of differential equations

Abstract

It is shown for a simple ODE that it has many symmetry groups beyond its usual Lie group symmetries, when its generalized solutions are considered within the nowhere dense differential algebra of generalized functions.