Modulation instability and periodic solutions of the nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: Modulation instability and periodic solutions of the nonlinear Schrödinger equation
zbMATH Open document ID: 0625.35015
DOI: 10.1007/BF01037866
author: V. I. Korneev
author: Nail Akhmediev
published in: Theoretical and Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: A very simple exact analytic solution of the nonlinear Schrödinger equation is found in the class of periodic solutions. It describes the time evolution of a wave with constant amplitude on which a small periodic perturbation is superimposed. Expressions are obtained for the evolution of the spectrum of this solution, and these expressions are analyzed qualitatively. It is shown that there exists a certain class of periodic solutions for which the real and imaginary parts are linearly related, and an example of a one-parameter family of such solutions is given.
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B20
zbMATH DE Number: 4015260
zbMATH Keywords: exact analytic solution
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: periodic solutions
zbMATH Keywords: time evolution
zbMATH Keywords: wave with constant amplitude
zbMATH Keywords: small periodic perturbation
zbMATH Keywords: spectrum
MaRDI profile type: Publication
cites work: Q5735118
description: scientific article; zbMATH DE number 4015260