Publication

Abstract : In this paper, we report existence of optical rouge waves in the focussingnon - autonomous nonlinear Schr¨odinger equation through numerical studiesof MI. The dynamics of non-autonomous rogue waves discussed and its associatedmodulation instability through linear stability analysis taken placefollowed by pulse splitting behaviour due to non - autonomous coefficient.We prove that the excitation of rogue waves with certain conditions in thebase band modulation instability regime. The above analysis of complexdynamics in terms of MI processes has allowed to experiments to excite thenonlinear superposition of rouge wave solutions using a modulated plane waveoptical field injected into optical fiber which offer the evidence for excitationof nonautonomous rogue waves in an inhomogeneous nonlinear medium. Itis identified from the results frequency modulation on a wavefield inducesmodulation instability as a result of rouge waves. We analyze the dependenceof parameters coeffiecient of GVD and nonlinearity (α(z)) and non- autonomous coefficient (β(z)) and the instability of rouge waves. Whenstudying rouge waves with the presence of non-autonomous coefficients canhave a profound impact on their behaviour, particularly in relation to theirself - steepening nature.