Abstract
We develop linear stability analysis (LSA) to quantitatively predict the dynamics of a perturbed plane wave in nonlinear systems. We take a nonintegrable fiber model with purely fourth-order dispersion as an example to demonstrate this method's effectiveness. For a Gaussian-type initial perturbation with cosine-type modulation on a plane wave, its propagation velocities, periodicity, and localization are predicted successfully, and the range of application is discussed. Importantly, the modulation-instability-induced growth of localized perturbation is proved different from the one of purely periodic perturbation and requires the modification of gain value for more accurate prediction. The method offers a needful supplement and improvement for LSA and paves a way to study the dynamics of a perturbed plane wave in more practical nonlinear systems.
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