Modulation instability analysis of a nonautonomous $$(3+1)$$-dimensional coupled nonlinear Schrödinger equation

Abstract

We investigate the modulation instability (MI) analysis of a nonautonomous (3+1)-dimensional coupled nonlinear Schrödinger (NLS) equation with timedependent dispersion and phase modulation coefficients. By employing standard linear stability analysis, we obtain an explicit expression for the MI gain as a function of dispersion, phase modulation, perturbation wave numbers and an initial incidence power. The nonautonomous coupled NLS equation is found to be modulationally unstable for the same sign of dispersion and phase modulation coefficients. This equation is modulationally stable for zero-dispersion and or phase modulation coefficients. But non-zero dispersion coefficient, it is modulationally stable/unstable on distinct bandwidth of wave numbers. The trigonometric, exponential, algebraic function of time and constant have been chosen as test functions for dispersion and phase modulation to find the effect on the MI analysis. The effect of focusing and defocusing medium on the MI analysis has also been investigated. The MI bandwidth in the focusing medium is found to be larger than defocusing medium. It is found that the modulation instability of the equation can be managed by proper choice of the dispersion and phase modulation parameters.

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

“…We shall seek a multi-harmonic solution by substituting into the system of Eqs. (46) the following Ansatz…”

“…Note that a similar analysis may be applied to incoherent pairs of CNLS equations [74] as well as to higher dimensional, non-autonomous CNLS equations [46].…”

“…Electron plasma (Langmuir) waves and ion acoustic waves [29,30,31], amidst other studies that focused mostly on electromagnetic modes [32,33,34,35,36,37,38]. 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 [39,40], coupled mixed-derivative NLS equations [41,42,43], variable coefficients CNLS equations [44], non-autonomous CNLS equations [45,46,47], systems involving four-wave mixing terms [48], coupled cubic-quintic NLS equations [49], space-shifted CNLS equations [50] and non-autonomous partially non-local CNLS equations [51], among others.…”