Orbital stability of standing waves for the nonlinear schrodinger equation with potential
Orbital stability of standing waves for the nonlinear schrodinger equation with potential
复制标题
非线性薛定谔方程的驻波轨道稳定性
DOI：
10.1142/s0129055x01001095
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发表时间：
2001
影响因子：
1.8
通讯作者：
P. Felmer
中科院分区：
文献类型：
--
作者：
C. Cid;P. Felmer
我们证明了非线性薛定谔方程 \[ i \ep \psi_t = \ep^2 \Delta \psi - V(x) \psi + f(|\psi|) \psi\quad \mbox{in}\quad \R^N \times (0,\infty)\,, \] 驻波的存在性和轨道稳定性，当普朗克常数 ℏ 足够小时，驻波集中在势能 V 的可能退化局部最小值附近。我们的方法适用于一般非线性，包括 f(s)=sp - 1 且 p ∈ (1,1 + 4/N)，但不要求极限方程的唯一性或非简并性。
We prove existence and orbital stability of standing waves for the nonlinear Schrodinger equation \[ i \ep \psi_t = \ep^2 \Delta \psi - V(x) \psi + f(|\psi|) \psi\quad \mbox{in}\quad \R^N \times (0,\infty)\,, \] concentrating near a possibly degenerate local minimum of the potential V, when the Plank's constant ℏ is small enough. Our method applies to general nonlinearities, including f(s)=sp - 1 with p ∈ (1,1 + 4/N), but does not require uniqueness nor non-degeneracy of the limiting equation.