Modulational instability of coupled waves in electronegative plasmas

Abstract

The dynamics of coupled ion-acoustic waves is investigated in an electronegative plasma made of Boltzmann negative ions, cold mobile positive ions and Boltzmann electrons. Using the reductive perturbation method, it is shown that the system can fully be described by a set of two coupled nonlinear Schrödinger equations. The parametric analysis of modulational instability reveals the existence of regions of instability that are sensitive to changes in plasma parameters such as the negative ion concentration ratio and the electron-to-negative ion temperature ratio. The analytical results are confronted to numerical simulations, where we examine the long-time dynamics of modulated waves in the electronegative plasma. One obtains the generation of nonlinear modulated waves that are sensitive to the negative-ion concentration ratio. Exact solutions for individual modes are discussed and one finally derives the coupled solution. The response of the latter to the plasma parameter variations is also addressed.

Impact of viscothermal loss on modulation instability and rogue waves in left-handed nonlinear diffractive acoustic transmission line metamaterials

“…Recent studies have been conducted on the solutions of nonlinear wave theory [21][22][23][24]. The nonlinear Schrödinger (NLS) equation has extensive physical applications in nonlinear optics [25], acoustics [7,12], plasma [26] and water waves [27]. Peregrine [28] gave the analytical expression of Rogue waves in the first-order as a result of MI on a constant wave background.…”

Numerical investigation on nonautonomous optical rogue waves and Modulation Instability analysis for a nonautonomous system

“…Rogue waves exist not only in ocean but also in various other fields, such as optics, superfluids, BoseEinstein condensates and so on. In the field of applied mathematics and nonlinear science, nonlinear Schrödinger (NLS) equations has received huge attention by theoretical and experimental physicists due to its potential applications in nonlinear optics [1][2][3][4][5], Bose-Einstein condensates (BEC) [6][7][8][9], plasma physics [10][11][12][13] and interaction of solitons in fiber optic communication [14]. In the physics of classical soliton, spectral parameter associated with inverse scattering transform (IST) of nonlinear evolution equation is not varying with time.…”

Coupled Nonlinear Schrodinger (CNLS) Equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

“…The consideration of two co-propagating wavepackets in a particular plasma fluid and their mutual interaction, results in a pair of coupled NLS (CNLS) equations, whose coefficients generally depend on the carrier wavenumber(s) of the respective carrier waves. Electron plasma (Langmuir) waves and ion acoustic waves [24,25,26], amidst other studies that focused mostly on electromagnetic modes [27,28,29,30,31,32,33]. Beyond plasma science, general forms of CNLS equations have been investigated in recent years with respect to the existence of vector solitons, breathers, and rogue wave solutions, in contexts including higher-order coupled NLS systems [34,35], coupled mixed-derivative NLS equations [36,37,38], variable coefficients CNLS equations [39], non-autonomous CNLS equations [40,41,42], systems involving four-wave mixing terms [43], coupled cubic-quintic NLS equations [44], space-shifted CNLS equations [45] and non-autonomous partially non-local CNLS equations [46], among others.…”