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Long-time validity of the Korteweg-de Vries approximation for the Boussinesq equation
We consider the Korteweg-de Vries (KdV) approximation for the good Boussinesq equation. Building upon the low-regularity local-in-time justification established by Hong and Yang \cite{HY2024}, we prove that this approximation remains valid on logarithmically long time intervals. The key ingredient i
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