The Inverse scattering transform fourier analysis for nonlinear problems
The Inverse scattering transform fourier analysis for nonlinear problems
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DOI：
10.1002/sapm1974534249
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发表时间：
1974-12
影响因子：
2.7
通讯作者：
M. Ablowitz;D. Kaup;A. Newell;H. Segur
中科院分区：
文献类型：
--
作者：
M. Ablowitz;D. Kaup;A. Newell;H. Segur
开发了一种系统方法，使人们能够识别某些重要类别的演化方程，这些方程可以通过逆散射方法求解。每个演化方程的形式由其相关线性化版本和积分微分算子的色散关系来表征。全面介绍了逆散射方法，并讨论了该解决方案的一般特征。给出了散射理论与贝克兰德变换的关系。鉴于色散关系的作用、相对简单的渐近态以及方法本身与傅里叶变换的相似性，该理论可以被认为是傅里叶分析对非线性问题的自然延伸。
A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering. The form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator. A comprehensive presentation of the inverse scattering method is given and general features of the solution are discussed. The relationship of the scattering theory and Backlund transformations is brought out. In view of the role of the dispersion relation, the comparatively simple asymptotic states, and the similarity of the method itself to Fourier transforms, this theory can be considered a natural extension of Fourier analysis to nonlinear problems.