On dummy variables of structure-preserving transformations

TL;DR

This paper introduces a method to derive equivalence subgroups of differential equations by leveraging simpler related equations, facilitating easier determination of their symmetry groups.

Contribution

It presents a novel approach to find equivalence subgroups using structure-preserving transformations, simplifying analysis of complex differential equations.

Findings

Method effectively derives equivalence subgroups from simpler equations

Applications demonstrate easier determination of symmetry groups

Examples include classical differential equations

Abstract

A method is given for obtaining equivalence subgroups of a family of differential equations from the equivalence group of simpler equations of a similar form, but in which the arbitrary functions specifying the family element depend on fewer variables. Examples of applications to classical equations are presented, some of which show how the method can actually be used for a much easier determination of the equivalence group itself.