Dispersive nonlinear geometric optics
Dispersive nonlinear geometric optics
复制标题
色散非线性几何光学
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. Rauch
中科院分区：
文献类型：
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作者：
P. Donnat;J. Rauch
我们构造无限精确的近似解的双曲型偏微分方程模型的短波长色散非线性现象。主要主题如下。(1)色散研究的自然框架是偏微分算子系统的波长解。自然的e-特征方程和e-程函方程是不齐次的。这正好与被称为群速度的传播速度取决于波数的长度这一事实相对应。(2)基本的动力学方程用算子方程表示。因此，增长或衰减往往以灾难性的速率ect/e发生。分析仅限于保守或接近保守的模型。(3)如果相位φ（x）/e满足自然e程函方程，则自然谐波相位nφ（x）/e通常不满足。人们需要对谐波施加一个相干假设。(4)在典型的例子中，谐波的集合...
We construct infinitely accurate approximate solutions to systems of hyperbolic partial differential equations which model short wavelength dispersive nonlinear phenomena. The principal themes are the following. (1) The natural framework for the study of dispersion is wavelength e solutions of systems of partial differential operators in e∂. The natural e-characteristic equation and e-eikonal equations are not homogeneous. This corresponds exactly to the fact that the speeds of propagation, which are called group velocities, depend on the length of the wave number. (2) The basic dynamic equations are expressed in terms of the operator e∂t. As a result growth or decay tends to occur at the catastrophic rate ect/e. The analysis is limited to conservative or nearly conservative models. (3) If a phase φ(x)/e satisfies the natural e-eikonal equation, the natural harmonic phases, nφ(x)/e, generally do not. One needs to impose a coherence hypothesis for the harmonics. (4) In typical examples the set of harmonics...