Some remarks about Lie and potential symmetries of a class of Korteweg-de Vries type equations

TL;DR

This paper investigates Lie and potential symmetries of a class of Korteweg-de Vries type equations, analyzing systems of determining equations to identify conditions under which potential symmetries exist.

Contribution

It introduces a method to distinguish between Lie and potential symmetries by analyzing three systems of determining equations for KdV-type equations.

Findings

Two systems yield only Lie symmetries.

The third system produces potential symmetries with specific structural conditions.

Potential symmetries depend on the equation's structure.

Abstract

Preliminary results about Lie and potential symmetries of a class of Korteweg-de Vries type equations are presented. In order to prove existence of potential symmetries three different systems of so called determining equations are analysed. It is shown that two systems lead only to Lie symmetries while the third system produces potential symmetries provided the equation in question has an appropriate structure