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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

Vol. 7 (2025), No. 1, 101–126
Abstract

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
Mathematical Subject Classification
Primary: 35C99, 47B35
Milestones
Received: 3 March 2024
Revised: 4 November 2024
Accepted: 17 December 2024
Published: 23 February 2025
Authors
Xi Chen
Institut de Mathématiques d’Orsay
Université Paris-Saclay
Orsay
France