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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Steep expulsive potentials in 1D and 2D Schrödinger equations support continuous spectra of normalizable bound states, including even/odd states in 1D and vortex states in 2D.
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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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The continuous spectrum of bound states in expulsive potentials
Steep expulsive potentials in 1D and 2D Schrödinger equations support continuous spectra of normalizable bound states, including even/odd states in 1D and vortex states in 2D.