Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
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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.
The Deng-Hani molecule reduction algorithm constructs a Kruskal spanning tree of the input molecule.
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Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System
Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
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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.
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Kruskal-style algorithm for cubic Schr\"odinger equation molecule reduction
The Deng-Hani molecule reduction algorithm constructs a Kruskal spanning tree of the input molecule.