English

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}
}
R2 v1 2026-06-28T07:23:52.546Z