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- W2952327557 abstract "We consider the cubic nonlinear Schrodinger (NLS) equation set on a two dimensional box of size $L$ with periodic boundary conditions. By taking the large box limit $L to infty$ in the weakly nonlinear regime (characterized by smallness in the critical space), we derive a new equation set on $R^2$ that approximates the dynamics of the frequency modes. This nonlinear equation turns out to be Hamiltonian and enjoys interesting symmetries, such as its invariance under Fourier transform, as well as several families of explicit solutions. A large part of this work is devoted to a rigorous approximation result that allows to project the long-time dynamics of the limit equation into that of the cubic NLS equation on a box of finite size." @default.
- W2952327557 created "2019-06-27" @default.
- W2952327557 creator A5045956945 @default.
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- W2952327557 date "2013-08-28" @default.
- W2952327557 modified "2023-09-27" @default.
- W2952327557 title "The weakly nonlinear large box limit of the 2D cubic nonlinear Schrodinger equation" @default.
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