Nonplanar dust acoustic waves in a four-component dusty plasma with double spectral distributed electrons: modulational instability and rogue waves

Abstract

A theoretical investigation of nonplanar (cylindrical and spherical) amplitude modulation of dust acoustic waves (DAWs) in a four component dusty plasma including positive and negative dusts, Maxwellian ions and double spectral electron distribution (DSED) is carried out. The focusing modified nonlinear Schrödinger equation (MNLSE) is derived using the derivative expansion perturbation technique (DEPT). The limit of DSED to Maxwell distribution is discussed. The effects of the two spectral indices, r and q , on the modulational instability (MI) growth rate are examined and it is deduced that increasing the value of r and q raises the MI growth rate. Additionally, the structure of the first and second-order dust acoustic (DA) rogue waves in the modulational unstable region is analyzed. The influences of both of r and q on the rogue wave amplitude (energy) are investigated. We found that increasing the value of r enhances the rogue wave amplitude while the opposite behavior is found by increasing q values. The findings of the present study are useful to interpret some physical phenomena in various plasma situations that found in space regions, such as Titan (the largest moon) of Saturn, auroral region and asteroid zones, where the effectiveness of non-Maxwellian particles such as DSED is existed.