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

Abstract

In this paper, we report existence of optical rogue waves in the focussing non - autonomous
nonlinear Schr ̈odinger equation (NLSE) through numerical studies of modulation instability (MI).
The dynamics of non-autonomous rogue waves discussed and its associated modulation instability
through linear stability analysis taken place followed by pulse splitting behaviour due to non -
autonomous coefficient. We prove that the excitation of rogue waves with certain conditions in the
base band modulation instability regime. The above analysis of complex dynamics in terms of MI
processes has allowed to experiments to excite the nonlinear superposition of rogue wave solutions
using a modulated plane wave optical field injected into optical fiber which offer the evidence for
excitation of nonautonomous rogue waves in an inhomogeneous nonlinear medium. It is identified
from the results frequency modulation on a wavefield induces modulation instability as a result of
rogue waves. We analyze the dependence of parameters coefficient of group velocity dispersion(GVD)
and nonlinearity (α(z)) and non - autonomous coefficient (β(z)) and the instability of rogue waves.
Our work suggests that the presence of non-autonomous coefficients can have a significant impact
on the emergence of extreme events, particularly in relation to their self - steepening nature.