A forced and damped Zakharov–Kuznetsov equation for a magnetized electron–positron–ion plasma affected by an external force is studied in this paper. Via the Hirota method, the soliton-like solutions are given. The soliton’s amplitude gets enhanced with the phase velocity ${\it\lambda}$ decreasing or ion-to-electron density ratio ${\it\beta}$ increasing. With the damped coefficient increasing, when the external force $g(t)$ is periodic, the two solitons are always parallel during the propagation and background of the two solitons drops on the $x{-}y$ plane, and amplitudes of the two solitons increase on the $x{-}t$ and $y{-}t$ planes, with $(x,y)$ as the coordinates of the propagation plane and $t$ as the time. When $g(t)$ is exponentially decreasing, the two solitons merge into a single one and the background rises on the $x{-}y$ plane, and amplitudes of the two solitons decrease on the $x{-}t$ and $y{-}t$ planes. Further, associated chaotic motions are obtained when $g(t)$ is periodic. Using the phase projections and Poincaré sections, we find that the chaotic motions can be weakened with ${\it\alpha}_{1}$, the amplitude of $g(t)$, decreasing. With ${\it\alpha}_{2}$, the frequency of $g(t)$, decreasing, a three-dimensional attractor with stretching-and-folding structure is found, indicating that the weak chaos is transformed into the developed chaos. Chaotic motions can also be weakened with ${\it\lambda}$, the phase velocity, decreasing, but strengthened with ${\it\beta}$, the ion-to-electron density ratio, and ${\it\alpha}_{2}$ decreasing.

The effect of a parallel viscous force induced damping and the magnetic precessional drift resonance induced damping on the stability of the resistive wall mode (RWM) is numerically investigated for one of the advanced steady-state scenarios in international thermonuclear experimental reactor (ITER). The key element of the investigation is to study how different plasma rotation profiles affect the stability prediction. The single-fluid, toroidal magnetohydrodynamic (MHD) code MARS-F (Liu et al., Phys. Plasmas, vol. 7, 2000, p. 3681) and the MHD–kinetic hybrid code MARS-K (Liu et al., Phys. Plasmas, vol. 15, 2008, 112503) are used for this purpose. Three extreme rotation profiles are considered: (a) a uniform profile with no shear, (b) a profile with negative flow shear at the $q=2$ rational surface ($q$ is the equilibrium safety factor), and (c) a profile with positive shear at $q=2$. The parallel viscous force is found to be effective for the mode stabilization at high plasma flow speed (about a few percent of the Alfven speed) for the no shear flow profile and the negative shear flow profile, but the stable domain does not appear with the positive shear flow profile. The predicted eigenmode structure is different with different rotation profiles. With a self-consistent inclusion of the magnetic precession drift resonance of thermal particles in MARS-K computations, a lower critical flow speed, i.e. the minimum speed needed for full suppression of the mode, is obtained. Likewise the eigenmode structure is also modified by different rotation profiles in the kinetic results.

The nonlinear propagation of positron-acoustic waves (PAWs) in an unmagnetized, collisionless, four component, dense plasma system (containing non-relativistic inertial cold positrons, relativistic degenerate electron and hot positron fluids as well as positively charged immobile ions) has been investigated theoretically. The Korteweg–de Vries (K–dV), modified K–dV (mK–dV) and further mK–dV (fmK–dV) equations have been derived by using reductive perturbation technique. Their solitary wave solutions have been numerically analysed in order to understand the localized electrostatic disturbances. It is observed that the relativistic effect plays a pivotal role on the propagation of positron-acoustic solitary waves (PASW). It is also observed that the effects of degenerate pressure and the number density of inertial cold positrons, hot positrons, electrons and positively charged static ions significantly modify the fundamental features of PASW. The basic features and the underlying physics of PASW, which are relevant to some astrophysical compact objects (such as white dwarfs, neutron stars etc.), are concisely discussed.

A nonlinear Zakharov–Kuznetsov (ZK) equation for ion acoustic solitary waves (IASWs) is derived using the reductive perturbation method (RPM) for magnetized plasmas in which the inertialess electrons and positrons are nonextensively $q$-distributed while ions are assumed to be warm and inertial. It is found that both compressive as well as rarefactive solitons coexist in the present model for different regions of non-extensive electron and positron parameters, $q_{e}$ and $q_{p}$. The magnetic field has no effect on the amplitude of the IASW, whereas the obliqueness angle of the wave propagation, the ion-to-electron temperature ratio ${\it\sigma}$ and positron-to-ion density concentration ratio $p$ affect both the amplitude and the width of the solitary wave structures. The transverse instability analysis illustrates that the one soliton solution has a constant growth rate, and it suffers from instability in the transverse direction. The relevance of the present study to astrophysical space plasmas is also discussed.