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.
Validity condition of normal form transformation for the β -FPUT system
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Survey compiling rigorous results on stability of FPU chains via Toda approximation, continuous KdV limits, and lower bounds on thermalization times from slow autocorrelation decay.
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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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A survey on rigorous results for the dynamics of periodic FPU chains
Survey compiling rigorous results on stability of FPU chains via Toda approximation, continuous KdV limits, and lower bounds on thermalization times from slow autocorrelation decay.