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 ina collisionless magnetized plasma with inertial positiveions, superthermal electrons and negatively chargedimmobile dust grains. By using the reductive perturbationtechnique, a 3D-nonlinear Schro¨dinger equation is derived,which governs the slow modulation of DIAW packets. Thelatter are found to be stable in the low-frequency (ω<ω(c))regime, whereas they are unstable for ω> ω(c), and themodulational instability is related to the modulationalobliqueness (0). Here, ω(ω(c)) is the nondimensional wave(ion-cyclotron) frequency. It is shown that the superthermalparameter j, the frequency ω(c) as well as the charged dustimpurity shift the MI domains around the ω–hplane, where l is the ratio of electron-to-ion number densities.Furthermore, it is found that the decay rate ofinstability is quenched by the superthermal parameter jwith cutoffs at lower wave number of modulation (K);however, it can be higher (lower) with increasing values of having cutoffs at higher values of K.