Premium
Long Time Behaviour of the Modulational Instability of Zakharov Equations
Author(s) -
Majumdar D.,
Bhakta J. C.
Publication year - 1985
Publication title -
beiträge aus der plasmaphysik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0005-8025
DOI - 10.1002/ctpp.19850250612
Subject(s) - modulational instability , perturbation (astronomy) , monochromatic color , physics , instability , nonlinear system , soliton , quantum electrodynamics , mathematical physics , quantum mechanics , optics
The long time behaviour of the modulational instability of a monochromatic Langmuir wave solution E 0 exp i ( k 0 x − ω 0 t ) of the Zakharov equations has been investigated. It is shown that near the threshold of linear instability the evolution of the modulational perturbation is governed by the nonlinear Schrödinger equation and thus the possibility of the development of the modulation into a train of soliton is established. In case of a purely growing modulational perturbation the long time behaviour of the perturbation is suggestive of a Fermi‐Pasta‐Ulam recurrence tendency.