Modulational instability of electron-acoustic waves in a plasma with Cairns–Tsallis distributed electrons

Small amplitude ion-acoustic solitary waves in a four-component magneto- rotating plasma with a modified Cairns-Tsallis distribution

“…In equation (7), if the electrostatic potential j is replaced by the normalized Ψ, the number density of the cold and hot electrons can be written, respectively, as…”

“…Propagation of ion acoustic solitary waves (IASWs) is usually related to the plasma compression. For this reason, more solitary wave properties are obtained from the compressive/rarefactive waves in multi-component magnetized [1][2][3][4] or unmagnetized [5][6][7] plasmas by using the pseudo potential approach and the reductive perturbation method, i.e., Korteweg-deVries (KdV) soliton [8,9], in the linear [10] and nonlinear dynamics [11,12]. It has been revealed that the KdV soliton are formed due to a balance between dispersion and nonlinearity in the plasma.…”

“…In order to fit the observations of astrophysical and space plasmas more accurately, a hybrid Cairns-Tsallis velocity distribution was proposed from nonextensive statistics [36,37], which provides the enhanced parameter flexibility for modeling the nonthermal plasmas with two parameters. There have been many works on the complex plasmas with the Cairns-Tsallis distribution [18,38,39], such as the modulational instability of electron-acoustic waves [7], the nonlinear dust acoustic waves [37], the effect of polarization force on oppositely charged dust grains in a magnetized plasma [38]. Most recently, based on the basic probability independence postulate in nonextensive statistics, a modified Cairns-Tsallis distribution was applied to the multi-component plasma with a potential [40].…”

An unmagnetized strongly coupled plasma: heavy ion acoustic shock wave excitations

“…They have also mentioned that nonthermality and nonextensivity may act concurrently on the nature (rarefactive or compressive) of the IA structures. Latter, the proper ranges of the nonextensive and nonthermal parameters are defined in [31][32][33][34] subject to the physical cutoff imposed by the monotonicity conditions q 5/7 and ( ) a = q 2 1 4 max for nonthermal-nonextensive case. Hence, one can use the (α, q)-velocity distribution to examine the physical issues observed in many SAEs by considering the appropriate ranges of α and q, that is, for (i) isothermal (q → 1 and α = 0), (ii) superthermal (α = 0, 0.33 < q < 1) and (iii) subthermal (α = 0, q > 1) but also (iv) nonthermal (q → 1 and 0 < α < 0.25) lighter plasma particles [31][32][33][34].…”

Modulation and nonlinear evolution of multi-dimensional Langmuir wave envelopes in a relativistic plasma

“…Over the last many years, the propagation of LWs received a great deal of attention [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] for research due to their potential application in different plasmas environments.In plasmas, the localization of nonlinear waves may occur in the form of an envelope pulse confining (modulating) carrier waves as governed by nonlinear Schrödinger (NLS)-like equations or solitons which are described by the Korteweg-de Vries (KdV)-like equations. These envelope solitons in plasmas are generically subject to their amplitude modulation due to self-interactions of plasma carrier waves [11,13,14,17,[21][22][23][24][25][26][27][28][29][30][31] (i.e., a slow variation of the wave envelope due to the nonlinearities). The formation of such envelope solitons is a result of the balance between the nonlinearity (self-focusing) and the wave dispersion.…”