Initial boundary value problem for Korteweg-de Vries equation: a review and open problems

TL;DR

This paper reviews the main results and open problems related to the initial boundary value problem for the Korteweg-de Vries equation, highlighting ongoing challenges in mathematical research over the past four decades.

Contribution

It provides a comprehensive overview of existing research and identifies key open problems in the study of the Korteweg-de Vries initial boundary value problem.

Findings

Summarizes 40 years of research on the IBVP for KdV.

Highlights unresolved mathematical challenges.

Proposes directions for future research.

Abstract

In the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note we present a review of the main results about this topic and also introduce interesting open problems which still requires attention from the mathematical point of view.