An explicit formula for the Benjamin--Ono equation
Analysis of PDEs
2023-11-08 v1
Abstract
We establish an explicit formula for the general solution of the Benjamin-Ono equation on the torus and on the line. Contents 1. Introduction 1 1.1. The Benjamin-Ono equation 1 1.2. The Lax pair 2 1.3. The explicit formula on the torus 3 1.4. The explicit formula on the line 3 1.5. Organization of the paper 4 2. Proof of the explicit formula on the torus 4 3. Proof of the explicit formula on the line 6 4. Final remarks 8 References 9
Keywords
Cite
@article{arxiv.2212.03139,
title = {An explicit formula for the Benjamin--Ono equation},
author = {Patrick Gerard},
journal= {arXiv preprint arXiv:2212.03139},
year = {2023}
}