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Explicit formula for the
Benjamin–Ono equation with square integrable and real valued
initial data and applications to the zero dispersion
limit
Xi Chen |
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Vol. 7 (2025), No. 1, 101–126
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Abstract |
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We extend Gérard’s formula for the solution of the Benjamin–Ono equation on the line to square integrable and real valued initial data. Combined with this formula, we also extend Gérard’s formula for the zero dispersion limit of the Benjamin–Ono equation on the line to more singular initial data. In the derivation of the extension of the formula for the zero dispersion limit, we also find an interesting integral equality, which might be useful in other contexts. |
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Keywords
Benjamin–Ono equation, explicit formula, zero dispersion
limit
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Mathematical Subject Classification
Primary: 35C99, 47B35
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Milestones
Received: 3 March 2024
Revised: 4 November 2024
Accepted: 17 December 2024
Published: 23 February 2025
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Authors |
| Xi Chen | |
| Institut de Mathématiques
d’Orsay Université Paris-Saclay Orsay France |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
