TY - JOUR
T1 - Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
AU - Buckmaster, T.
AU - Germain, P.
AU - Hani, Z.
AU - Shatah, J.
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/9
Y1 - 2021/9
N2 - Consider the cubic nonlinear Schrödinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation, predicted in wave turbulence theory, on a nontrivial timescale.
AB - Consider the cubic nonlinear Schrödinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation, predicted in wave turbulence theory, on a nontrivial timescale.
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U2 - 10.1007/s00222-021-01039-z
DO - 10.1007/s00222-021-01039-z
M3 - Article
AN - SCOPUS:85103045890
SN - 0020-9910
VL - 225
SP - 787
EP - 855
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -