Nonlinear evolution of the modulational instability and chaos using one-dimensional Zakharov equations and a simplified model

Journal Article · Tue Feb 01 04:00:00 EST 2005 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.1850477· OSTI ID:20698336

Sharma, R P; Batra, K; Verga, A D ^[1]

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1. Centre for Energy Studies, Indian Institute of Technology, New Delhi 110016 (India)

Nonlinear evolution of modulational instability by using the nonlinear Schroedinger equation in one dimension reveals a periodic reoccurrence of initial conditions. The nonlinear Schroedinger equation is the adiabatic limit of Zakharov equations, which couples the electrostatic electron plasma wave and ion-acoustic wave propagation. In the present paper nonlinear evolution of modulational instability is investigated by using one-dimensional Zakharov equations numerically. A simplified model is predicted that establishes the fact that the effect of relaxing the condition of adiabaticity is drastic on the nonlinear evolution patterns of modulational instability. These evolutions are quite sensitive to initial conditions, Fermi-Pasta-Ulam recurrence is broken up and a chaotic state develops. Next, quantitative methods like calculation of Lyapunov exponents and their variation with wave number is used to study spatial and temporally chaotic behavior. It is shown that regular patterns with a periodic sequence in space and time and spatiotemporal chaos with irregular localized patterns are formed in different regions of unstable wave numbers.

• OSTI ID: 20698336
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 2 Vol. 12; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ELECTRON PLASMA WAVES
ION ACOUSTIC WAVES
LYAPUNOV METHOD
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PLASMA INSTABILITY
SCHROEDINGER EQUATION