Extreme spectral asymmetry of Akhmediev breathers and Fermi-Pasta-Ulam recurrence in a Manakov system

Classification of beating solitons, their physical spectra, and second-order nonlinear superpositions

We obtained the full set of multiparameter vector beating soliton solutions for Manakov equations in both focusing and defocusing cases. Based on exact solutions, physical spectra of beating solitons are calculated analytically. It is found that the spectra of moving beating solitons are asymmetric relative to the sign change of the frequency. In contrast, the static beating solitons have symmetric spectra. We also study the second-order vector beating soliton solutions with either equal or unequal velocities. Numerical simulations confirmed the validity of our exact solutions.

Fundamental and Second-Order Superregular Breathers in Vector Fields

We developed an exact theory of the superregular breathers (SRBs) of Manakov equations. We have shown that the vector SRBs do exist both in the cases of focusing and defocusing Manakov systems. The theory is based on the eigenvalue analysis and on finding the exact links between the SRBs and modulation instability. We have shown that in the focusing case the localized periodic initial modulation of the plane wave may excite both a single SRB and the second-order SRBs involving four fundamental breathers.

Fermi-Pasta-Ulam-Tsingou recurrence and cascading mechanism for resonant three-wave interactions

Evolution of resonant three-wave interaction is governed by quadratic nonlinearities. While propagating localized modes and inverse scattering mechanisms have been studied, transient states such as rogue waves and breathers are not fully understood. Modulation instability modes can trigger growth of disturbances and the eventual development of breathers. Here we study computationally the dynamics beyond the first formation of breathers, and demonstrate repeating patterns of breathers as a manifestation of the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT). While nonlinearity governs the actual dynamics, the range of wave numbers for modulation instability remains a useful indicator. Depending on the stability characteristics of the fundamental mode and the higher-order harmonics ("sidebands"), "regular" and "staggered" FPUT patterns can arise. A "cascading mechanism" provides analytical verification, as the fundamental and sideband modes attain the same magnitude at one particular instant, signifying the first occurrence of a breather. A triangular spectrum is also computed, similar to experimental observations of optical pulses. Such spectra can elucidate the spreading of energy among the sidebands and components of the triad resonance. The concept of "effective energy" is examined and the eigenvalues of the inverse scattering mechanism are computed. Both approaches are utilized to correlate with the occurrence of regular or staggered FPUT. These numerical and analytical studies can enhance our understanding of wave interactions in fluid mechanics and optics.

Self-Frequency Shift in Transmission of Asymmetric Pulse in Optical Medium

Linear and nonlinear effects often induce a pulse self-frequency shift as it propagates along with an optical medium. Here, we theoretically investigate the transmission dynamics of asymmetric pulses propagating along with an optical medium in the temporal and spectral domains. Due to the asymmetric nonlinear phase-shift effect in the optical medium, the peak wavelength of asymmetric pulses exhibits a redshift or a blueshift in the spectral domain, while it slows down or speeds up in the temporal domain. Our results show that the peak wavelength shift initiated by a temporal or spectral asymmetric pulse depends not only on the pulse intensity, but also on the initial pulse chirp and dispersion of optical medium. We find that the peak wavelength shift of the asymmetric pulse increases with the pulse intensity and the initial pulse chirp, together with the spectrum width. The temporal and frequency shifts of the asymmetric pulses are found to be sensitive to the asymmetry ratio as well. These excellent properties may lead to the realization of a self-frequency shift-based tunable light source by launching asymmetric pulses into an optical medium.