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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A large deviations principle is established for rogue waves in the cubic nonlinear Schrödinger equation with randomized quasi-periodic initial data in dimensions d>1, holding for times O(ε^{-1-η}) under polynomial Fourier decay.
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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.
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Large Deviations for the Nonlinear Schrodinger Equation with Randomized Quasi-Periodic Initial Data in Higher Dimensions: Beyond the Critical Time Scale
A large deviations principle is established for rogue waves in the cubic nonlinear Schrödinger equation with randomized quasi-periodic initial data in dimensions d>1, holding for times O(ε^{-1-η}) under polynomial Fourier decay.