The solitonic, periodic and quasiperiodic solutions that obey the full system of transport equations describing one-dimensional motion of a isotropic collisionless quasineutral plasma in a magnetic field are treated. The domains of physical parameters of such a plasma are determined for fast and slow magnetoacoustic branches, where solitary waves and generalized solitary waves exist. In the parameter domain where solitary waves are replaced by non-local generalized solitary waves, the localized disturbances are subject to decay, which has qualitatively different mechanisms for fast and slow magnetoacoustic waves. The specific feature of the decay process for fast waves is found to be characterized by a decrease of energy of the disturbance due to quasistationary radiation of a resonant periodic wave of the same nature. Analogous disturbances, having the form of a slow magnetoacoustic solitary wave core, practically do not radiate resonant Alfvénic modes, but rapidly lose energy as a result of continuous shedding of a slow-wave component. Various types of shock waves are also considered. Their structure is formed by existing solitonic configurations – solitary and generalized solitary waves. Possibilities of observations of solitary waves and their decay in a real plasma are discussed.

The transient Hartmann flow of an electrically conducting viscous incompressible non-Newtonian power-law fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer, without neglecting the Hall effect. A sudden uniform and constant pressure gradient, an external uniform magnetic field that is perpendicular to the plates, and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures, while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing nonlinear momentum and energy equations are obtained using finite difference approximations. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions as well as the dissipation terms are examined.

Electrical breakdown in a mixed gas is investigated. The plasma at breakdown is evaluated in terms of the mole fraction χ. The optimum condition for the highest plasma density is described in terms of the ionization energy and collisional cross-section of the mixed gas. The optimum mole fraction for the highest plasma density is found to be χ = 0.03 for the case of plasma generation in neon gas mixed with xenon for a plasma display panel. The optimum condition for the highest number of electronic excitations is also obtained.

The technique for analytical investigation of the Alfvén resonance, proposed by Dmitrienko [J. Plasma Phys.57, 311 (1997); 62, 145 (1999)] is used to obtain the matching conditions and to calculate the rate of resonant absorption and heating in a nonlinear dissipative resonance layer. It is shown that one matching condition is the invariability condition for the coefficient of the singular part of the solution describing the MHD mode outside the resonance layer, and the other condition is a jump of the coefficient of a regular solution, the value of which depends on the ratio of the dissipative to nonlinear spatial scales. It is established that the ratio of the jump of the imaginary part of the regular solution to the coefficient of the singular solution is exactly equal to the rate of resonant heating, and this heating is calculated as a function of the ratio of the linear dissipative to nonlinear scales. The resonant absorption coefficient is calculated as well. It is shown that the nonlinearity leads to a decrease of the heating rate and the absorption coefficient compared with those predicted by linear theory.

The effect of an external magnetic field Bext on the propagation of an electromagnetic wave pulse incident on a nonlinear medium is studied. It is shown that all the incident energy can be reflected in a large domain of Bext (self-screening), if the incident wave is in pulsed form. Having a complicated behavior, the reflection coefficient shows total transmission or self-screening in the intermediate range of the external magnetic field.