Selected aspects of the Korteweg-de Vries equation

TL;DR

This paper provides an overview of selected aspects of the Korteweg-de Vries (KdV) equation, focusing on integrable partial differential equations and their properties, based on lecture notes from courses taught over five years.

Contribution

It compiles and discusses key features and insights about the KdV equation, emphasizing its role in integrable PDEs, with educational intent.

Findings

Highlights integrability properties of the KdV equation

Summarizes analytical techniques for solving KdV

Provides educational insights into integrable PDEs

Abstract

These lecture notes grew out of notes for courses around Integrable PDEs and the KdV equation given by the authors during the past five years at the University of Antwerp (Belgium). Comments and suggestions are welcome.