Modern Physics Letters B

In this paper, we consider coupled variable coefficients nonlinear Schrödinger equations (VCNLS), which can be used to describe the interaction among the modes in nonlinear optics and Bose–Einstein condensation. With the help of a gauge transformation of the spectral problem, the generalized Darboux transformation (DT) for the VCNLS is constructed. As an application of the generalized DT, we first derive the second-order and third-order semi-rational solutions of the VCNLS. In addition, we investigate the dynamics of the second-order and third-order semi-rational solutions with different coefficients. Finally we find that the coefficients $D(t)$ and $R(t)$ mainly affect the shape of the above solutions, while the amplification or absorption coefficient ${𝒯}(t)$ will change the amplitude. The obtained results will enrich the study of theory of the nonlinear localized waves.

Chromium-doped CaMgSi₂O₆ (${\mathrm{\text{Cr}}}^{3+}$: CMS) fluorescent ceramics with various concentrations were fabricated using solid-state reaction technique. All the samples were sintered at 1250${}^{\circ }$C for 3 h. Analysis of microstructure of the Cr${}^{3+}$: CMS ceramics shows homogeneous structure with grain size distributions between 0.86 nm and 2.26 nm. Luminescent spectra of the ceramics show two emission peaks, a strong peak at 872 nm and a weak peak at 960 nm because of ${}^4{T}_2\to {}^4{A}_2$ transition of the Cr${}^{3+}$ ions. Intensity of the emission peaks increases with Cr${}^{3+}$ concentration, reaches maximum with 0.1 at.% Cr${}^{3+}$, then decreases with higher Cr${}^{3+}$ concentration. Owing to the differences in crystal field strength, the luminescent properties of the Cr${}^{3+}$: CMS fluorescent ceramics and powder are quite different.

As a kind of new intelligent materials, liquid crystal elastomer (LCE) has attracted widespread interest. In this paper, we introduce LCE into chiral phononic crystal (CPC), and investigate the properties of band structures based on the iterative calculation method. The effects of dextral bending angle, chiral geometric parameters $b$ and $h$, and the director rotation angle on bandgaps are mainly discussed. This work is a meaningful try for application of LCE in acoustic field and propose a new strategy in designing of PC with tunable bandgaps.

To explore the mechanism among disturbance, spatiotemporal evolution characteristics and stability for traffic flow, this paper presents an improved lattice hydrodynamic model with lane change into consideration and investigates the influence of three influencing factors, namely, lane change effect, predictive effect, and self-delayed flux integral effect on traffic flow. Moreover, theoretical analyses containing linear and nonlinear analysis are further developed. By linear stability analysis, we obtain the model’s neutral stability curve. Moreover, the Burgers equation and modified Korteweg–de Vries equation are derived in nonlinear stability analysis section. The phase transition of traffic flow and its propagation behavior of congestion near the critical point are described. In addition, under the influence of disturbance, the spatiotemporal evolution characteristics of density wave and energy consumption are intuitively shown by numerical simulations. The results reveal that appropriate lane change behavior, predictive effect and self-delayed flux integral effect are conducive to improve traffic stability and reduce energy consumption.

In this paper, we study the dynamics properties of three-component antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results are obtained by numerical simulations of the spinor Gross–Pitaevskii equation. We find that the population of the spin components is seriously influenced by magnetic field. The dynamical evolution process is accelerated in the presence of magnetic field. As a result, the periodic oscillation of spin exchange dynamics emerges and the components $m_f=\pm 1$ have the same amplitude. In addition, the density profile displays that the influences of dipolar interaction are masked by magnetic field. Moreover, we introduce an order parameter to characterize the disorder-order crossover, where it is seen that the system develops toward the disordered state with strong dipole strength when magnetic field is included.