INVERSE SCATTERING TRANSFORM-FOURIER ANALYSIS FOR NONLINEAR PROBLEMS.

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

Research output: Contribution to journalArticlepeer-review

1884 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 languageEnglish (US)
Pages (from-to)249-315
Number of pages67
JournalStudies in Applied Mathematics
Volume53
Issue number4
DOIs
StatePublished - Jan 1 1974
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics

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