We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.

We investigate the half-Skyrmion excitations induced by spin-orbit coupling in the rotating and rapidly quenched spin-1 Bose-Einstein condensates. We give three expressions of the corresponding spin vectors to describe the half-Skyrmion. Our results show that the half-Skyrmion excitation depends on the combination of spin-orbit coupling and rotation, and it originates from a dipole structure of spin which is always embedded in three vortices constructed by each condensate component respectively. When both the strength of spin-orbit coupling and rotation frequency are larger than some critical values, the half-Skyrmions encircle the center with one or several circles to form a radial lattice, which occurs even in the strong ferromagnetic/antiferromagnetic condensates. We can use both the spin-orbit coupling and the rotation to adjust the radial lattice. The realization and the detection of the half-Skyrmions are compatible with current experimental technology.

The nonequilibrium dynamics of a rapidly quenched spin-1 Bose gas with spin-orbit coupling is studied. By solving the stochastic projected Gross-Pitaevskii equation, we show that crystallization of half-skyrmions (merons), can occur in a spinor condensate of 87 Rb. The stability of such a crystal structure is analyzed. Likewise, inverted half-skyrmions can be created in a spin-polarized spinor condensate of 23 Na. Our studies provide a chance to explore the fundamental properties of skyrmionlike matter.

We study analytically the characteristics of optical absorption and slow-light solitons in an asymmetrical fourlevel N configuration semiconductor quantum wells with the cross-coupling relaxation of longitudinal-optical phonons (CCRLOP). It is shown that, in the linear range, the electromagnetically induced transparency (EIT) depends on the coherence control of both the optical fields and the CCRLOP. A double EIT is obtained under a relatively strong optical field which is from the hole and antibonding states in the wide well. Especially, the double EIT becomes perfect under the condition of increasing the CCRLOP. In the nonlinear range, the CCRLOP has an important effect on both the amplitude and the group velocity of the solitons. The amplitude of solitons reveals parabolic changes which obtain a maximum value with the increase of CCRLOP. The group velocity of the solitons continuously slows down if there are fixed three-photon detunings. These results may have potential applications for all-optical switching and some optical information engineering in solid systems.