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

Abstract

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 3Dnonlinear Schrödinger (NLS) 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 (MI) is related to the modulational obliqueness (θ ). Here, ω (ω c ) 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 ω − θ 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 cut-offs at lower wave number of modulation (K), however, it can be higher (lower) with increasing values of µ (ω c ) having cut-offs at higher values of K.