Solitons and the Inverse Scattering Transform
Solitons and the Inverse Scattering Transform
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DOI：
10.1007/978-0-8176-8265-1_9
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
L. Debnath
中科院分区：
文献类型：
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作者：
L. Debnath
色散和非线性在自然界的波动中起着基本的作用。在完全忽略色散的非线性浅水方程中，随着垂直剖面的发展，会出现典型的双曲型断裂现象。特别是，Korteweg-de Vries方程中的线性色散项阻止了这种情况在其解中发生。一般来说，在浅水理论中加入色散效应可以防止断裂。非线性理论对非线性如何影响色散波动的问题提供了一些见解。另一个有趣的特征是初始均匀波剖面的不稳定性和随后的调制。
Dispersion and nonlinearity play a fundamental role in wave motions in nature. The nonlinear shallow water equations that neglect dispersion altogether lead to breaking phenomena of the typical hyperbolic kind with the development of a vertical profile. In particular, the linear dispersive term in the Korteweg–de Vries equation prevents this from ever happening in its solution. In general, breaking can be prevented by including dispersive effects in the shallow water theory. The nonlinear theory provides some insight into the question of how nonlinearity affects dispersive wave motions. Another interesting feature is the instability and subsequent modulation of an initially uniform wave profile.