Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves
Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves
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DOI：
10.1155/s1073792804132340
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发表时间：
2003-08
影响因子：
1
通讯作者：
S. Gustafson;K. Nakanishi;Tai-Peng Tsai
中科院分区：
文献类型：
--
作者：
S. Gustafson;K. Nakanishi;Tai-Peng Tsai
研究了一类非线性薛定谔方程的小孤波解族。考虑能量空间H1中的小尺度解，将其分解为孤立波分量和色散波分量。目的是建立孤立波的渐近稳定性和色散波的渐近完备性。也就是说，当t → ∞时，孤立波分量收敛到固定孤立波，而色散分量在H1中强收敛到自由薛定谔方程的解.
We study a class of nonlinear Schrodinger equations which admit families of small solitary wave solutions. We consider solutions which are small in the energy space H 1 , and decompose them into solitary wave and dispersive wave components. The goal is to establish the asymptotic stability of the solitary wave and the asymptotic completeness of the dispersive wave. That is, we show that as t → ∞, the solitary wave component converges to a fixed solitary wave, and the dispersive component converges strongly in H 1 to a solution of the free Schrodinger equation.