ON THE DYNAMICS OF DUST-ACOUSTIC AND DUST-CYCLOTRON FREAK WAVES IN A MAGNETIZED DUSTY PLASMA

The modulational instability of dust-acoustic wave (DAW) and dustcyclotron wave (DCW) in a three-component plasma that consists of dust, ions, and electrons in a magnetized dusty plasma is investigated. Moreover, the freak/rogue waves creation and propagation of DAW and DCW in the present plasma system are reported. Electrons and ions both follow the Maxwellian distribution, while the negatively charged dust is taken to be dynamic. For studying MI, a nonlinear Schrodinger equation (NLSE) is obtained using the Krylov-Bogoliubov-Mitropolsky method. The MI criterion for the NLSE is defined precisely and investigated numerically for DAW and DCW. The stable and unsteady regions of the modulated wave packets were accurately quantified based on the relevant physical parameters. The effects of relevant physical parameters namely, the magnetic field intensity, electron to dust density concentration ratio, ratios of effective temperature to electrons and ions temperature, and angle of wave propagation on both stable and unstable regions of DAW and DCW are examined numerically. It is found that, within unstable regions, a random perturbation of the amplitude grows and thus leads to a creation of freak/rogue waves. In order to demonstrate the effects of the physical parameters on the rogue waves (RWs) profile, the relevant numerical analysis of the rational solution of the NLSE is presented. Also, the higher-order solutions/or the super RWs are reported. The possible observation of propagation of fundamental RWs and super RWs in space plasmas and in laboratory experiments is also pointed out.