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.
On the wave turbulence theory for a stochastic KdV type equat ion – General- ization for the inhomogeneous kinetic limit
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Introduces the complex mZK equation on T² and proves local well-posedness in Sobolev spaces together with failure of uniform continuity of the data-to-solution map.
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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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Complex-valued modified Zakharov Kuznetsov equation
Introduces the complex mZK equation on T² and proves local well-posedness in Sobolev spaces together with failure of uniform continuity of the data-to-solution map.