Influence of perturbation amplitude and perturbation frequency on Fermi-Pasta-Ulam-Tsingou recurrence phenomenon

Abstract

Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomenon refers to the property of a multimode nonlinear system returning to the initial states after complex stages of evolution. The FPUT recurrence phenomenon closely links with modulation instability (MI) by employing the perturbed continuous waves as the initial condition. When the perturbation frequency is located inside the MI spectra, then the perturbed CWs are unstable and the perturbations will grow up with evolution. This nonlinear MI evolution results in the FPUT phenomenon. In this work, we explore in detail the effects of perturbation amplitude and perturbation frequency on the FPUT recurrence phenomena numerically, which has never been studied systematically, to the best of our knowledge. Using the results of our studies, we find that the perturbation amplitude can significantly affect the FPUT phenomenon. Firstly, the number of FPUT cycles is very sensitive to the perturbation amplitude. Large (small) perturbation amplitude can result in much more (much less) FPUT cycles. Secondly, very irregular (regular) FPUT wave evolution together with the corresponding spectra evolution can be observed at relatively large (small) values of perturbation amplitude, where the unequal (equal) distances are observed between adjacent maximum wave amplitudes spatially in the background of optical fibers. In contrast, the effects of perturbation frequency on the FPUT cycles are relatively minor, and the maximum FPUT cycles are observed at perturbation frequencies around the optimal modulation frequency generating the peak MI gain. However, the perturbation frequency can drastically affect the number of high-order sidebands excited at the distances of periodic maximum wave amplitude formation. We find that larger perturbation frequency leads to much fewer high-order sidebands. According to our studies, for observing FPUT conveniently and observing more FPUT cycles, the perturbation amplitude of the input signal should be as large as possible and the perturbation frequency should be around the optimum modulation frequency. We should also emphasize that the large perturbation amplitude results in irregular FPUT patterns with unequal distances between adjacent maximum wave amplitude formations spatially in the background of optical fibers, and large perturbation frequency results in much less high-order sidebands. Our results will provide very helpful information for the FPUT observation in experiment, and should arouse the interest of the readers in nonlinear physics.