The Weakly Nonlinear Schr\"odinger Equation in Higher Dimensions with
Quasi-periodic Initial Data
The Weakly Nonlinear Schr\"odinger Equation in Higher Dimensions with
Quasi-periodic Initial Data
In this paper, under the exponential/polynomial decay condition in Fourier space, we prove that the nonlinear solution to the quasi-periodic Cauchy problem for the weakly nonlinear Schr\"odinger equation in higher dimensions will asymptotically approach the associated linear solution within a specific time scale. The proof is based on a combinatorial …