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The dispersion characteristics of the circularly polarized electromagnetic waves propagating along a homogeneous magnetic field in a dusty plasma have been investigated theoretically. The Vlasov equation has been employed to find the response of the magnetized plasma particles where the dust grains form a static background of highly charged and massive centers having certain correlation. It is found that in addition to the usual Landau damping which is negligible in the low temperature approximation, a novel mechanism of damping of the Alfven waves due to the dust comes into play. The modification and damping of the Alfven waves depend on the dust perturbation parameters, unequal densities of plasma particles, the average correlation length of the dust grains, temperature of the plasma and the magnetic field.

A nonlinear evolution equation governing the two dimensional propagation of fast and slow magnetosonic modes in a warm collisional plasma has been derived. This equation is a combination of Kadomtsev-Petviashvili (K-P) equation and the Burgers equation. The two dimensional K-P equation has two types of solitary wave solutions depending on the sign of the coefficients. One type is the usual planar type, the other is the lump solution. Both types of solitary wave solutions decay with time in the weak collisional limit. The two dimensional features of the amplitude and width of the lump or algebraic soliton have been discussed and the decay rates computed numerically. The decay rates depend on plasma beta and on the angle of propagation and the rates are different for the fast and the slow waves. At a certain angle of propagation the decay rates of both the modes are equal in the case of low beta plasma. Because of 2-D effects, the slow mode, although it has a lower collisional decay rate than the fast mode,...

The magnetohydrodynamic stability of streaming tearing mode is investigated numerically. A bulk plasma flow parallel to the antiparallel magnetic field lines and localized in the neutral sheet excites a streaming tearing mode more strongly than the usual tearing mode, particularly for the wavelength of the order of the neutral sheet width (or smaller), which is stable for the usual tearing mode. Interestingly, examination of the eigenfunctions of the velocity perturbation and the magnetic field perturbation indicates that the streaming tearing mode carries more energy in terms of the kinetic energy rather than the magnetic energy. This suggests that the streaming tearing mode instability can be a more feasible mechanism of plasma acceleration than the usual tearing mode instability.

A model equation as above (Boussinesq form) which governs the lattice wave and shallow water waves, has been reduced to a modified form of Hirota equation for intermediate range of wave number ( k