On Short-Scale Oscillatory Tails of Long-Wave Disturbances
On Short-Scale Oscillatory Tails of Long-Wave Disturbances
复制标题
长波扰动的短尺度振荡尾部
DOI：
10.1002/sapm19959411
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发表时间：
1995
影响因子：
2.7
通讯作者：
T.
中科院分区：
文献类型：
--
作者：
T. Akylas;T.
本文以强迫Korteweg-de Vries方程为简单模型，给出了一个计算定常长波扰动引起的短尺度振荡尾巴振幅的摄动法。在弱色散的极限下，这些尾巴的振幅呈指数级小，超出了通常长波展开的所有数量级。结果表明，通过在波数域工作，可以非常简单地确定尾部幅度，而不需要在复平面上进行渐近匹配。诱导出的短波尾部对长波剖面的细节很敏感。该方法适用于非局部孤立波和其他需要使用指数渐近的问题。
Using the forced Korteweg‐de Vries equation as a simple model, a perturbation procedure is presented for calculating the amplitude of short‐scale oscillatory tails induced by steady long‐wave disturbances. In the limit of weak dispersion, these tails have exponentially small amplitude that lies beyond all orders of the usual long‐wave expansion. It is demonstrated that by working in the wavenumber domain, the tail amplitude can be determined quite simply, without the need for asymptotic matching in the complex plane. The induced short‐wave tail is sensitive to the details of the long‐wave profile. The proposed technique is applicable to nonlocal solitary waves and to other problems that require the use of exponential asymptotics.