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math.AP2019
Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
Tristan Buckmaster, Pierre Germain, Zaher Hani +1
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…
math.AP2013
Nonlinear resonances with a potential: Multilinear estimates and an application to NLS
Pierre Germain, Zaher Hani, Samuel Walsh
This paper considers the question of global in time existence and asymptotic behavior of small-data solutions of nonlinear dispersive equations with a real potential . The main…