The processes of soliton generation and interference focus on the complex nonlinear soliton dynamics resembling matter particles. In order to further understand the dynamic process of solitons from a multidimensional perspective, here we report the vectorial solitons nature under two-sets pulse splitting in a single cavity induced by dual-core fiber assisted ultrafast fiber lasers. Owing to the weakly coupled cores in symmetrical dual core fiber (SDCF), two pulse groups interaction are formed in a cavity. By using the dispersive Fourier transformation technique (DFT), it was found that the four-component polarized rotation vector solitons (PRVS) generate. Moreover, gradually increasing the power can obtain the locked soliton bound state in two core space, and the corresponding evolution is similar to that of non-degenerate bright solitons in Bose Einstein condensates (BEC). In addition, by properly controlling the soliton phase offset in SDCF, the soliton rain state of multi pulse evolution can be obtained. The related experimental results would be fruitful to the communities interested in soliton dynamics and frequency comb lasers.

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.