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We present recent results from Gérard (Tunis J Math 5(3):593–603, 2023, [22]) and Gérard (The zero dispersion limit for the Benjamin–Ono equation on the line, [23]) establishing an explicit formula for every regular enough solution of the Benjamin–Ono equation on the line, and solving the corresponding problem of the small dispersion limit. We discuss some perspectives open by this formula.

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The Benjamin–Ono Equation on the Line: Explicit Formula and Small Dispersion Limit

  • 会议论文

  • 发表日期：

    2025年

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  • Patrick Gérard

摘要

We present recent results from Gérard (Tunis J Math 5(3):593–603, 2023, [22]) and Gérard (The zero dispersion limit for the Benjamin–Ono equation on the line, [23]) establishing an explicit formula for every regular enough solution of the Benjamin–Ono equation on the line, and solving the corresponding problem of the small dispersion limit. We discuss some perspectives open by this formula.