Dissipative electrostatic wave modulation in warm multi-ion dusty plasmas with superthermal electrons

A theoretical investigation has been carried out to explore the modulational instability (MI) of electrostatic waves in a warm multi-ion dusty plasma system containing positive ions, negative ions and positively or negatively charged dust in presence of superthermal electrons. With the help of the standard perturbation technique, it is found that the dynamics of the modulated wave is governed by a damped nonlinear Schrödinger equation (NLSE). Regions of MI of the electrostatic wave are precisely determined and the analytical solutions predict the formation of dissipative bright and dark solitons as well as dissipative first- and second-order rogue wave solutions. It is found that the striking features (viz., instability criteria, amplitude and width of rogue waves, etc.) are significantly modified by the effects of relevant plasma parameters such as degree of the electron superthermality, dust density, etc. The time dependent numerical simulations of the damped NLSE reveal that modulated electrostatic waves exhibit breather like structures. Moreover, phase plane analysis has been performed to study the dynamical behaviors of NLSE by using the theory of dynamical system. It is remarked that outcome of present study may provide physical insight into understanding the generation of several types of nonlinear structures in dusty plasma environments, where superthermal electrons, positive and negative ions are accountable (e.g. Saturn’s magnetosphere, auroral zone, etc.).

Modulational Instability of Ion-Acoustic Waves in Pair-Ion Plasma

The modulational instability (MI) of ion-acoustic waves (IAWs) is examined theoretically in a four-component plasma system containing inertialess electrons featuring a non-thermal, non-extensive distribution, iso-thermal positrons, and positively as well as negatively charged inertial ions. In this connection, a non-linear Schrödinger equation (NLSE), which dominates the conditions for MI associated with IAWs, is obtained by using the reductive perturbation method. The numerical analysis of the NLSE reveals that the increment in non-thermality leads to a more unstable state, whereas the enhancement in non-extensivity introduces a less unstable state. It also signifies the bright (dark) ion-acoustic (IA) envelope solitons mode in the unstable (stable) domain. The conditions for MI and its growth rate in the unstable regime of the IAWs are vigorously modified by the different plasma parameters (viz., non-thermal, non-extensive q-distributed electron, iso-thermal positron, the ion charge state, the mass of the ion and positron, non-thermal parameter α, the temperature of electron and positron, etc.). Our findings may supplement and add to prior research in non-thermal, non-extensive electrons and iso-thermal positrons that can co-exist with positive as well as negative inertial ions.

Modulational instability and rogue waves in one-dimensional nonlinear acoustic metamaterials: case of diatomic model

In this paper, by means of the expanded Taylor series and Lindstedt-Poincar ́e perturbation methods, the coupled nonlinear Schrödinger equations (CNLSE) modeling the propagation of acoustic waves in acoustic metamaterial is obtained. Using these equations, the Modulational Instability (MI) phenomenon is observed in disturbance mode. Manakov integrable system is derived with suitable parameters and we shown that the Rogue Waves (RWs) can propagate diatomic acoustic metamaterials.