A large deviations principle is proven for the supremum of KdV solutions over polynomial timescales, with phase quasi-synchronization identified as the dominant mechanism for extreme amplitudes in the integrable regime.
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Almost global large deviations principle for the KdV equation
A large deviations principle is proven for the supremum of KdV solutions over polynomial timescales, with phase quasi-synchronization identified as the dominant mechanism for extreme amplitudes in the integrable regime.