Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

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 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 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 1 , in the presence and absence of negative ions.

Modulational instability of coupled waves in electronegative plasmas

“…For the specific case of ENPs, such dependence is supported by the plots of figure 2, where the coefficients m 1 , m 2 and m 3 are plotted versus the wavenumber k, when ENP parameters change. We note from figure 2(a) that for any value of α, the dispersion coefficients m 1 remains negative, as already reported in some recent works [16,17,[18][19][20]. However, figure 2(b) shows that the coefficient of nonlinearity m 2 is also negative in some intervals of k, when a = 0.1 and a = 0.4, but becomes positive when > k k cr,1 .…”

“…Several contributions have pointed out the importance of the balance between nonlinearity and dispersion in the formation of IAWs in ENPs [13][14][15]. Especially, their modulational instability (MI) has been addressed by a few authors, with interest in the way some plasma parameters, such as the electron-to-negative ion temperature ratio and the negative ion concentration ratio, may affect the formation of modulated IAWs [16,17,[18][19][20]. Among the partial differential equations that support the propagation of such waves, the nonlinear Schrödinger (NLS) equation remains the most famous, as it has been extensively derived from different plasma models [18][19][20].Its generalized version such as the Davey-Stewartson equations were also derived, and their solutions discussed [21,22].…”

Ion Acoustic Waves in Weakly Relativistic Plasma—Separation of Relativistic and Electron-Temperature Effects

“…In recent years, works that account for small relativistic effects have been published. In some works, a lowest order analysis led to the KdV [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] or the Nonlinear Schrödinger equation [16][17]. In others, the analysis went as far as generating the KdV equation with a first-order perturbation [18][19][20].…”

“…They have been called obstacles to asymptotic integrability [21][22][23][24][25][26][27][28][29][30][31][32][33]. The previous studies of weak relativistic effects [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have missed these effects as they did not perform a second order analysis.…”

“…This has been done in the literature with the scaling of Eqs. (5) and (6) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. It will be also adopted here, but with the scaling of Eq.…”