A perturbation theory for Alfvén solitons
type: Item
instance of: scholarly article
title: A perturbation theory for Alfvén solitons
zbMATH Open document ID: 0595.35030
DOI: 10.1016/0167-2789(84)90280-X
author: Einar Mjølhus
author: J. Wyller
published in: Physica D
publication date: 1984-01-01T00:00:00Z
review text: A perturbation method for the perturbed DNLS-equation \[ (1)\quad q_ t+\{| q|^ 2q\}_ x+iq_{xx}=\sigma Q_ 1[q],\quad 0<\sigma <<1 \] is presented, where \(Q_ 1[q]=q_{xx}\). By using the inverse scattering transform which has been obtained in the paper of \textit{D. J. Kaup} and \textit{. A. C. Newell} [J. Math. Phys. 19, 798-801 (1978; Zbl 0383.35015)] for equation (1) as \(\sigma =0\), the authors obtained the correspondence between Alfvén solitons and eigenvalues for the perturbed DNLS equation (1), and discuss some properties of Alfvén solitons.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81Q15
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 78A45
zbMATH DE Number: 3957744
zbMATH Keywords: derivative nonlinear Schrödinger equation
zbMATH Keywords: Alfvén solitons
reviewed by: Boling Guo
MaRDI profile type: Publication
cites work: A Perturbation Expansion for the Zakharov–Shabat Inverse Scattering Transform
cites work: Perturbation analysis of single Langmuir solitons
cites work: Q4151274
cites work: An exact solution for a derivative nonlinear Schrödinger equation
cites work: The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
cites work: Q3864448
cites work: Q5682682
cites work: Modified nonlinear Schrödinger equation for Alfvén waves propagating along the magnetic field in cold plasmas
full work available at URL: 0167-2789(84)90280-x
OpenAlex ID: W2007130964
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description: scientific article; zbMATH DE number 3957744