Abstract
The main objective of our study consists in revealing the role of the cubic–quintic nonlinearity in the dynamics of induced modulational instability in nonautonomous nonlinear optical systems with dispersion and nonlinearity varying along the propagation distance. Analytical methods are used to obtain the criterion of modulational instability in the cubic–quintic nonautonomous systems. Nonlinear stage of the modulational instability is studied by direct computational modeling. The main results of our computer experiments clearly demonstrate the imperfect spectral energy restoration leading to variations of the Fermi–Pasta–Ulam recurrence (“déjà vu”) periods. The significance of the results consists in the important possibility of suppressing the appearance of rogue waves due to the compensation mechanisms for both the quintic nonlinearity and the changing dispersion.
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