Evolution of solitonless wave packets in the nonlinear Schrödinger equation and the Korteweg-de Vries equation with dissipative perturbations
type: Item
instance of: scholarly article
title: Evolution of solitonless wave packets in the nonlinear Schrödinger equation and the Korteweg-de Vries equation with dissipative perturbations
zbMATH Open document ID: 0618.35098
DOI: 10.1007/BF01037865
author: B. A. Malomed
published in: Theoretical and Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: Nonlinear Schrödinger (for both repulsive and attractive cases), Korteweg-de Vries and sine-Gordon equations with small dissipative perturbing terms are considered. Near the linear instability threshold, where nonlinear and spatially inhomogeneous dissipation dominates, explicit solutions expressing local amplitude and occupation numbers of a nonsoliton (dispersive) wavetrain in terms of arbitrary initial data are obtained at sufficiently large times in the logarithmic approximation. For the nonlinear Schrödinger equation with the repulsion, the particular case of the wavetrain near the soliton production threshold is also considered.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4002682
zbMATH Keywords: Nonlinear Schrödinger
zbMATH Keywords: Korteweg-de Vries
zbMATH Keywords: sine-Gordon equations
zbMATH Keywords: small dissipative perturbing terms
zbMATH Keywords: explicit solutions
zbMATH Keywords: nonsoliton (dispersive) wavetrain
zbMATH Keywords: logarithmic approximation
zbMATH Keywords: soliton production threshold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4002682