Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

We show that the nonlinear stage of the dual-wavelength pumped modulation instability(MI)in nonlinear Schrödinger equation(NLSE)can be effectively analyzed by mode truncation methods.The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves.Significantly,the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure.It is demonstrated that there has much richer dynamic behavior,in contrast to the nonlinear waves reported before.This novel nonlinear wave promises to inject new vitality into the study of MI.

Modulation Instability and Non-Degenerate Akhmediev Breathers of Manakov Equations

We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on the frequency-wavenumber plane.Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate.

Transient breathing dynamics during extinction of dissipative solitons in mode‑locked fiber lasers

The utilization of the dispersive Fourier transformation approach has enabled comprehensive observation of the birth process of dissipative solitons in fiber lasers.However,there is still a dearth of deep understanding regarding the extinction process of dissipative solitons.In this study,we have utilized a combination of experimental and numerical techniques to thoroughly examine the breathing dynamics of dissipative solitons during the extinction process in an Er-doped mode-locked fiber laser.The results demonstrate that the transient breathing dynamics have a substantial impact on the extinction stage of both steady-state and breathing-state dissipative solitons.The duration of transient breathing exhibits a high degree of sensitivity to variations in pump power.Numerical simulations are utilized to produce analogous breathing dynamics within the framework of a model that integrates equations characterizing the population inversion in a mode-locked laser.These results corroborate the role of Q-switching instability in the onset of breathing oscillations.Furthermore,these findings offer new possibilities for the advancement of various operational frameworks for ultrafast lasers.

Solitons in the fractional Schr?dinger equation with parity-time-symmetric lattice potential

We investigate the properties of spatial solitons in the fractional Schr?dinger equation(FSE) with parity-time(PT)-symmetric lattice potential supported by the focusing of Kerr nonlinearity. Both one-and two-dimensional solitons can stably propagate in PT-symmetric lattices under noise perturbations. The domains of stability for both one-and two-dimensional solitons strongly depend on the gain/loss strength of the lattice. In the spatial domain, the solitons are rigidly modulated by the lattice potential for the weak diffraction in FSE systems. In the inverse space, due to the periodicity of lattices, the spectra of solitons experience sharp peaks when the values of wavenumbers are even. The transverse power flows induced by the imaginary part of the lattice are also investigated, which can preserve the internal energy balances within the solitons.