KdV shock-like waves as invariant solutions of KdV equation symmetries

TL;DR

This paper investigates the invariance of shock-like waves in the KdV equation under certain symmetries, proposing a hypothesis and illustrating the approach with Burgers equation as an example.

Contribution

It introduces a hypothesis that KdV shock-like waves are invariant under specific symmetry combinations and demonstrates this approach using Burgers equation.

Findings

Shock-like waves in KdV are invariant under Galilean and higher symmetries.

The approach is exemplified with Burgers equation.

Provides a new perspective on symmetry-invariant solutions in nonlinear wave equations.

Abstract

We consider the following hypothesis: some of KdV equation shock-like waves are invariant with respect to the combination of the Galilean symmetry and KdV equation higher symmetries. Also we demonstrate our approach on the example of Burgers equation.