具有三波相互作用的非线性薛定谔方程组驻波的不稳定性

Pub Date : 2009-01-01 DOI:10.1619/FESI.52.371

M. Colin, T. Colin, Masahito Ohta

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引用次数: 31

摘要

我们考虑与等离子体中拉曼放大有关的非线性薛定谔方程的三组分系统。在N≤3维，我们研究了形式为(0,0,e2iωtψ)的驻波解的轨道不稳定性，其中ψ是标量非线性薛定谔方程的基态。我们使用时间导数代替空间导数来估计非线性项，改进了我们之前的论文[4]中的一个不稳定性结果，并且给出了一个更简单的证明。

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Instability of Standing Waves for a System of Nonlinear Schrodinger Equations with Three-Wave Interaction

We consider a three-component system of nonlinear Schrodinger equations related to the Raman amplification in a plasma. In dimension N ≤ 3, we study the orbital instability of standing wave solution of the form (0,0,e2iωtψ), where ψ is a ground state of scalar nonlinear Schrodinger equation. Using time derivative instead of space derivatives to estimate nonlinear terms, we improve an instability result in our previous paper [4], and also give a simpler proof.

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