On the Benjamin-Ono equation on $\mathbb{T}$ and its periodic and quasiperiodic solutions

TL;DR

This paper surveys recent results on the Benjamin-Ono equation on the torus, focusing on constructing large families of periodic and quasiperiodic solutions that lack smoothness.

Contribution

It introduces new methods to construct non-smooth periodic and quasiperiodic solutions for the Benjamin-Ono equation on the torus.

Findings

Constructed large families of non-smooth solutions

Developed new analytical methods

Extended understanding of solution structures

Abstract

In this paper, we survey our recent results on the Benjamin-Ono equation on the torus. As an application of the methods developed we construct large families of periodic or quasiperiodic solutions, which are not $C^\infty$-smooth.