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.

We consider a magnetized dusty plasma, which composed of low-temperature and high-temperature ions, electrons, and dust particles. The dynamical behaviors can be described by a (3+1)-dimensional Zakharov–Kuznetsov equation (ZKE). Interestingly, a type of completely localized solitary waves, which are different from the line solitons, of ZKE are obtained analytically and approximately for the first time. This kind of solitary wave is also confirmed numerically by the Petviashvili method. Both the analytical and numerical results indicate that the amplitude of the localized wave is proportional to its velocity and inverse proportional to the nonlinear interaction strength. A finite difference scheme with second-order accuracy is presented to make the long-time nonlinear evolution of ZKE. The numerical results indicate that the localized solitons are always dynamically stable. Moreover, the collision between two solitary waves is investigated numerically. The results show that both elastic and inelastic collision exist when two localized solitary waves colliding.

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.

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