Instability of standing waves for non-linear Schrödinger-type equations
Instability of standing waves for non-linear Schrödinger-type equations
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DOI：
10.1017/s014338570000938x
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发表时间：
1988-12
影响因子：
0.9
通讯作者：
C. Jones
中科院分区：
文献类型：
--
作者：
C. Jones
本文证明了一个定理，给出了非线性薛定谔型方程的某些驻波解线性不稳定的条件。线性化算子在驻波处的本征方程可以用动力系统方法分析。一个积极的特征值，然后示出存在的拍摄参数在拉格朗日平面的空间。该定理适用于光波导中出现的情况。
Abstract A theorem is proved giving a condition under which certain standing wave solutions of non-linear Schrödinger-type equations are linearly unstable. The eigenvalue equations for the linearized operator at the standing wave can be analysed by dynamical systems methods. A positive eigenvalue is then shown to exist by means of a shooting argument in the space of Lagrangian planes. The theorem is applied to a situation arising in optical waveguides.