Abstract
Relativistic ion-acoustic waves are investigated in an electronegative plasma. The use of the reductive perturbation method summarizes the hydrodynamic model to a nonlinear Schrödinger equation which supports the occurrence of modulational instability (MI). From the MI criterion, we derive a critical value for the relativistic parameter alpha _{1}, below which MI may develop in the system. The MI analysis is then conducted considering the presence and absence of negative ions, coupled to effects of relativistic parameter and the electron-to-negative ion temperature ratio. Under high values of the latter, additional regions of instability are detected, and their spatial expansion is very sensitive to the change in alpha _{1} and may support the appearance of rogue waves whose behaviors are discussed. The parametric analysis of super-rogue wave amplitude is performed, where its enhancement is debated relatively to changes in alpha _{1}, in the presence and absence of negative ions.
Highlights
Envelope solitons, generic solutions of the nonlinear Schrödinger (NLS) equation, have been extensively studied during the past 30 years, due to their fundamental importance in nonlinear physics
Generic solutions of the nonlinear Schrödinger (NLS) equation, have been extensively studied during the past 30 years, due to their fundamental importance in nonlinear physics. Based on their localization properties, breather solitons have been used as models of rogue waves (RWs) whose behaviors and characteristics are not yet fully unmasked, mainly because they may appear suddenly, propagate within short times, destroy everything on their way and disappear without any trace [1, 2]
Quite a limited number of works have been devoted to electronegative plasmas (ENPs), including the contributions by Ghim and Hershkowitz [34] and Mamun et al [35], where the existence of ion-acoustic waves (IAWs) and dust-acoustic waves (DAWs) was addressed in ENPs containing Boltzmann negative ions, Boltzmann electrons and cold mobile positive ions
Summary
Generic solutions of the nonlinear Schrödinger (NLS) equation, have been extensively studied during the past 30 years, due to their fundamental importance in nonlinear physics. From recent contributions, when only positive ions are taken into consideration, the nonlinear terms of the Korteweg–de Vries (KdV) equation are positive, and one may obtain only compressive solitary waves [31], whereas in the presence of both positive and negative ions, soliton characteristics considerably change, due to the nonlinear response of the system to the presence of negative ions [32, 33] This is indubitably related to the charge neutrality condition which changes, leading to a decrease in the number of electrons and a decrease in their subsequent shielding effect. Quite a limited number of works have been devoted to ENPs, including the contributions by Ghim and Hershkowitz [34] and Mamun et al [35], where the existence of ion-acoustic waves (IAWs) and dust-acoustic waves (DAWs) was addressed in ENPs containing Boltzmann negative ions, Boltzmann electrons and cold mobile positive ions The response of such waves, solutions of the KdV equation, to external magnetic fields was studied [32, 33].
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