摘要:

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 problem

ISSN:0022-2526    

DOI:10.1002/sapm1974534249

年代:1974

数据来源: WILEY

摘要:

The nonlinear interactions and modulations of ann‐dimensional wave and of a disturbance to a near‐critical system governed by a general (n+ 1)‐dimensional system of equations are studied by perturbation methods. It is found that these modulations are governed by an evolution equation which is either by itself or coupled to a second equation, depending on the nature of the long wave solutions of the corresponding linearized system. When a single evolution equation exists, its leading terms are shown to give the nonlinear Schrödinger equation. Water waves and near‐critical plane Poiseuille flow are discussed as

ISSN:0022-2526    

DOI:10.1002/sapm1974534317

年代:1974

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1974534337

年代:1974

数据来源: WILEY