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- W2740819319 abstract "In this paper, we prove a Nekhoroshev type theorem for high dimensional NLS (nonlinear Schrodinger equations):[ mathrm{i} partial_{t} u - Delta u + V * u + partial_{overline{u}} g(x,u,overline{u}) = 0, quad x in mathbb{T}^d, ; t in mathbb{R} ] where real-valued function $V$ is sufficiently smooth and $g$ is an analytic function. We prove that, for any given $M in mathbb{N}$, there exists an $varepsilon_0 gt 0$, such that for any solution $u = u(t,x)$ with initial data $u_0 = u_0(x)$ whose Sobolev norm $|u_{0}|_{s} = varepsilon lt varepsilon_0$, during the time $|t| leq varepsilon^{-M}$, its Sobolev norm $|u(t)|_s$ remains bounded by $C_s varepsilon$." @default.
- W2740819319 created "2017-08-08" @default.
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- W2740819319 date "2017-10-01" @default.
- W2740819319 modified "2023-10-16" @default.
- W2740819319 title "A Nekhoroshev Type Theorem of Higher Dimensional Nonlinear Schrödinger Equations" @default.
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- W2740819319 doi "https://doi.org/10.11650/tjm/7951" @default.
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