Linear and nonlinear properties of an obliquely propagating dust magnetosonic wave

Linear and nonlinear properties of the two-dimensional obliquely propagating dust magnetosonic wave are studied in a three-component dusty plasma. The dispersion relations in the linear and Kadomstev–Petviashvili (KP) equation in the nonlinear regime are derived for small-amplitude perturbations. It is shown that the linear dispersion properties of the low-frequency dust magnetosonic wave depend on the angle θ that the magnetic field makes with the x-axis, the ratio of ion to electron concentration, and the plasma beta. It is found that retaining the electron pressure term gives rise to novel features in the dust magnetosonic wave. The slow magnetosonic wave is found to be the damped mode and, therefore, the only propagating mode in our system is the fast magnetosonic mode. It is found that the KP equation admits compressive solitary structures. Finally, it is found that the amplitude of the soliton increases as the ratio of electron to ion concentration, p, angle θ, and the plasma beta, β, is increased.