On unique continuation for non-local dispersive models

TL;DR

This paper reviews and discusses unique continuation properties for solutions to various nonlinear non-local dispersive evolution equations, including models like Benjamin-Ono and Camassa-Holm, highlighting recent results and open questions.

Contribution

It provides a comprehensive review and discussion of unique continuation results for a broad class of nonlinear non-local dispersive models, including new insights and open problems.

Findings

Review of unique continuation properties for non-local dispersive models

Discussion of recent results and techniques in the field

Identification of open questions and future research directions

Abstract

We consider unique continuation properties of solutions to a family of evolution equations. Our interest is mainly on nonlinear non-local models. This class contains the Benjamin-Ono, the Intermediate Long Wave, the Camassa-Holm, the dispersion generalized Benjamin-Ono and non-local Schr\"odinger equations as well as their generalizations. We shall review, discuss, expand, and comment on several results. In addition, we shall state some open questions concerning these results and their techniques.