NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms
NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms
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具有拟线性二次项的方程的时间振荡长波的 NLS 近似
DOI：
10.1002/mana.201200325
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发表时间：
2015
影响因子：
1
通讯作者：
G. Schneider
中科院分区：
文献类型：
--
作者：
M. Chirilus;Wolf‐Patrick Düll;G. Schneider
考虑一类具有拟线性二次非线性的非线性波动方程。底层载波ei（k0x−ω0t）包络的缓慢时空调制可以用NLS方程正式描述。本文的目的是提出一种方法，可以证明在k0=0情况下拟线性波动方程的形式近似和真解之间的误差估计。本文首次证明了一类拟线性二次项非线性波动方程的NLS近似的有效性。
We consider a nonlinear wave equation with a quasilinear quadratic nonlinearity. Slow spatial and temporal modulations of the envelope of an underlying carrier wave ei(k0x−ω0t) can be described formally by an NLS equation. It is the purpose of this paper to present a method which allows to prove error estimates between this formal approximation and true solutions of the quasilinear wave equation in case k0=0 . The paper contains the first validity proof of the NLS approximation for a nonlinear wave equation with quasilinear quadratic terms.