The stability properties of dark solitons in quasi-one-dimensional Bose–Einstein condensate (BEC) loaded in a Jacobian elliptic sine potential with three-body interactions are investigated theoretically. The solitons are obtained by the Newton-Conjugate Gradient method. A stationary cubic-quintic nonlinear Schrödinger equation is derived to describe the profiles of solitons via the multi-scale technique. It is found that the three-body interaction has distinct effect on the stability properties of solitons. Especially, such a nonlinear system supports the so-called dark solitons (kink or bubble), which can be excited not only in the gap, but also in the band. The bubbles are always linearly and dynamically unstable, and they cannot be excited if the three-body interaction is absent. Both stable and unstable kinks, depending on the physical parameters, can be excited in the BEC system.

The propagation characteristics of terahertz waves in high-temperature magnetized inhomogeneous plasma sheath were investigated theoretically by the shift operator finite difference time domain method. Both the transmission characteristics of left and right circularly polarized terahertz waves propagating in uniform or non-uniform plasma were analyzed. Simulation results reveal that the transmission characteristics of terahertz waves in plasma will be influenced by plasma parameters and the external magnetic field. The plasma sheath has a high pass filtering characteristic to terahertz waves, which provides a significant theoretical basis, to a certain extent, for the “blackout” problem.

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We numerically and theoretically investigated the completely localized solitons, obtained by the Petviashvili method, and their dynamical stabilities in a magnetized dusty plasma with trapped ions. The results suggest that its amplitudes are proportional to the square of its speed and inversely proportional to the square of the nonlinear interaction strength, which are also confirmed analytically. The dependence of the soliton amplitudes on various physical parameters is investigated systematically. Numerical results indicate that the localized solitons are always dynamically stable. When two localized solitons collide, their amplitudes and phase are nearly invariant. However, if a stable localized soliton collides with an unstable line soliton, the latter will evolve into a series of completely localized solitons.