Induced modulational instability in the sign-reversal dispersion traps: Imperfect Fermi–Pasta–Ulam recurrence and partial “déjà vu” phenomenon

Abstract Our direct computer experiments reveal the main features of the induced modulational instability in the sign-reversal dispersion traps and offer a clearer view of how nonlinear analogies to the “deja vu” phenomena have arisen. We demonstrate the crucial role of the higher-order dispersion in the origin of the imperfect Fermi–Pasta–Ulam recurrence and partial “deja vu” phenomena. Induced modulational instability can be used to generate the steady-state soliton trains in the sign-reversal parabolic dispersion traps with exponentially decreasing dispersion.