Amplitude modulation of three-dimensional low-frequency solitary waves in a magnetized dusty superthermal plasma

The amplitude modulation of three-dimensional (3D) dust ion-acoustic wave (DIAW) packets is studied in a collisionless magnetized plasma with inertial positive ions, superthermal electrons and negatively charged immobile dust grains. By using the reductive perturbation technique, a 3D-nonlinear Schrödinger equation is derived, which governs the slow modulation of DIAW packets. The latter are found to be stable in the low-frequency (ω< ω_c) regime, whereas they are unstable for ω> ω_c, and the modulational instability is related to the modulational obliqueness (θ). Here, ω(ωc) is the nondimensional wave (ion-cyclotron) frequency. It is shown that the superthermal parameter κ, the frequency ω_c as well as the charged dust impurity (0 < μ< 1) shift the MI domains around the plane, where μ is the ratio of electron-to-ion number densities. Furthermore, it is found that the decay rate of instability is quenched by the superthermal parameter κ with cutoffs at lower wave number of modulation (K); however, it can be higher (lower) with increasing values of μ(ω_c) having cutoffs at higher values of K.