Generation of breathing solitons in the propagation and interactions of Airy–Gaussian beams in a cubic–quintic nonlinear medium

Using the split-step Fourier transform method, we numerically investigate the generation of breathing solitons in the propagation and interactions of Airy–Gaussian（AiG） beams in a cubic–quintic nonlinear medium in one transverse dimension. We show that the propagation of single AiG beams can generate stable breathing solitons that do not accelerate within a certain initial power range. The propagation direction of these breathing solitons can be controlled by introducing a launch angle to the incident AiG beams. When two AiG beams accelerated in opposite directions interact with each other,different breathing solitons and soliton pairs are observed by adjusting the phase shift, the beam interval, the amplitudes,and the light field distribution of the initial AiG beams.

Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential

We investigate the explicit novel localized nonlinear matter waves of the cubic-quintic nonlinear Schr6dinger equation with spafiotemporal modulation of the nonlinearities and the harmonic-lattice potential using a modified similarity trans- formation. We also find that when the modulus of the Jacobian elliptic function in the limit closes to 1, the shapes of the breathing solitons may exhibit some interesting features, i.e., one breathing soliton dividing into two in the ground state. The stability of the exact solutions is investigated numerically such that some stable breathing soliton solutions are found.

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.

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose–Einstein Condensates with Two- and Three-Body Interactions

Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.