Modulational instability and associated ion-acoustic modulated envelope solitons in a quantum plasma having ion beams

This work employs the one-dimensional quantum hydrodynamic model to investigate the nonlinear propagation of modulated ion-acoustic waves (IAWs) in unmagnetized quantum plasma with ion beams. A reductive perturbation technique (RPT) is carried out to reduce the set of fluid equations to a cubic nonlinear Schrödinger equation (NLSE), which governs the propagation of the modulational instability (MI) and its associated modulated structures (envelope solitons). It is demonstrated that plasma configurational parameters, such as ion beam density, quantum diffraction parameter, and ion beam temperature, significantly affect MI and the related nonlinear structures. We also examined the impact of these pertinent physical parameters on the critical wavenumber and the growth rates related to MI. The critical wavenumber and MI growth rate were found to decrease with growing values of quantum diffraction parameters and ion beam temperature while falling with ion beam density. Furthermore, the modulated nonlinear localized structures that appear as bright and dark envelope solitons are discussed in detail. Our results are expected to reveal the mystery of the behavior of the modulated nonlinear phenomena that may arise and propagate in such a type of quantum plasma with ion beams. Moreover, the results can be used to understand the behavior of many modulated nonlinear phenomena and then devote them to various applications.