INVERSE SCATTERING TRANSFORM-FOURIER ANALYSIS FOR NONLINEAR PROBLEMS.

Mark J. Ablowitz; David J. Kaup; Alan C. Newell; Harvey Segur

doi:10.1002/sapm1974534249

INVERSE SCATTERING TRANSFORM-FOURIER ANALYSIS FOR NONLINEAR PROBLEMS.

Mark J. Ablowitz, David J. Kaup, Alan C. Newell, Harvey Segur

Research output: Contribution to journal › Article › peer-review

2291 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	249-315
Number of pages	67
Journal	Studies in Applied Mathematics
Volume	53
Issue number	4
DOIs	https://doi.org/10.1002/sapm1974534249
State	Published - 1974
Externally published	Yes

ASJC Scopus subject areas

Applied Mathematics

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10.1002/sapm1974534249

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title = "INVERSE SCATTERING TRANSFORM-FOURIER ANALYSIS FOR NONLINEAR PROBLEMS.",

abstract = "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.",

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AB - 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.

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INVERSE SCATTERING TRANSFORM-FOURIER ANALYSIS FOR NONLINEAR PROBLEMS.

Abstract

ASJC Scopus subject areas

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