Computation of the direct scattering transform for the nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: Computation of the direct scattering transform for the nonlinear Schrödinger equation
zbMATH Open document ID: 0761.65093
DOI: 10.1016/0021-9991(92)90370-E
author: Guido Boffetta
author: Alfred R. Osborne
published in: Journal of Computational Physics
publication date: 1993-01-17T00:00:00Z
review text: The paper presents a numerical algorithm for determining the direct scattering transform of a narrow-banded wave train, described by the nonlinear Schrödinger equation. The direct scattering transform may be interpreted as the nonlinear Fourier spectrum of the complex envelope function of the wave train. Connections to previous numerical approaches are done. The approach is generalized to include several nonlinear wave equations as the Korteweg- de Vries, sine-Gordon and sinh-Gordon equations.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 98368
zbMATH Keywords: spectral method
zbMATH Keywords: numerical algorithm
zbMATH Keywords: sinh-Gordon equations
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: sine-Gordon equation
zbMATH Keywords: direct scattering transform
zbMATH Keywords: narrow-banded wave train
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: nonlinear Fourier spectrum
zbMATH Keywords: nonlinear wave equations
reviewed by: Laura Iulia Aniţa
MaRDI profile type: Publication
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full work available at URL: 0021-9991(92)90370-e
OpenAlex ID: W2073185643
description: scientific article; zbMATH DE number 98368