References & Citations
Mathematics > Analysis of PDEs
Title: Explicit formula for the Benjamin--Ono equation with square integrable and real valued initial data and applications to the zero dispersion limit
(Submitted on 20 Feb 2024 (v1), last revised 26 Apr 2024 (this version, v3))
Abstract: In this paper, we extend G{\'e}rard'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 the G{\'e}rard'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.
Submission history
From: Xi Chen [view email][v1] Tue, 20 Feb 2024 10:45:46 GMT (14kb)
[v2] Thu, 25 Apr 2024 13:42:20 GMT (14kb)
[v3] Fri, 26 Apr 2024 07:42:40 GMT (14kb)
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