Modulational instability of dust-ion-acoustic waves and associated first and second-order rogue waves in a super-thermal plasma
A proper theoretical research has been carried out to explore the modulational instability (MI) conditions of dust-ion-acoustic (DIA) waves (DIAWs) in a three-component dusty plasma system containing inertialess κ -distributed electrons, and inertial warm positive ions and negative dust grains. The nonlinear Schrödinger equation (NLSE) has been derived by employing the reductive perturbation method. The numerical analysis under consideration demonstrates two types of modes, namely, fast and slow DIA modes. The MI conditions of DIAWs and the configuration of the energetic rogue waves (RWs) associated with DIAWs in the modulationally unstable parametric regime have been rigorously changed by the variation of various plasma parameters, namely, charge, mass, temperature, and number density of the plasma species. The findings of our present investigation will be useful in understanding the criteria for the formation of electrostatic RWs in both astrophysical environments (viz., Jupiter's magnetosphere, cometary tails, pulsar magneto-sphere, interstellar medium, Earth's mesosphere, Saturn's rings, etc.) and laboratory experiments.