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arXiv · 2212.03139

An explicit formula for the Benjamin--Ono equation

Patrick Gerard
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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

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Patrick Gerard. 2022-12-06. An explicit formula for the Benjamin--Ono equation. https://doi.org/10.2140/tunis.2023.5.593

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