Justification of modulation equations for hyperbolic systems via normal forms
Justification of modulation equations for hyperbolic systems via normal forms
复制标题
通过范式证明双曲系统调制方程的合理性
DOI：
10.1007/s000300050034
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
G. Schneider
中科院分区：
文献类型：
--
作者：
G. Schneider
抽象的。考虑了非线性薛定谔方程作为小幅度的几乎空间周期波列的调制方程的合理性问题。我们展示了原始系统的解与通过非线性薛定谔方程的解获得的近似值之间的精确估计。通过范式变换，消除了所考虑的双曲系统的先验危险二次项。然后变换后的系统从三次项开始。这允许通过简单应用格朗沃尔不等式来证明非线性薛定谔方程的合理性。此外，还估计了共振的影响。
Abstract. The justification problem for the Nonlinear Schrödinger equation as a modulation equation for almost spatial periodic wavetrains of small amplitude is considered. We show exact estimates between solutions of the original system and their approximations which are obtained by the solutions of the Nonlinear Schrödinger equation. By a normal form transform the a priori dangerous quadratic terms of the considered hyperbolic systems are eliminated. Then the transformed systems start with cubic terms. This allows to justify the Nonlinear Schrödinger equation by a simple application of Gronwall's inequality. Moreover, the influence of resonances is estimated.