Nonplanar ion-acoustic Gardner solitons in a pair-ion plasma with nonextensive electrons and positrons

Higher-order nonlinear equations for the electron-acoustic waves in a nonextensive electron-positron-ion plasma

“…planetary rings, solar winds (Kopp et al 1997), stellar polytropes (Plastino and Plastino 1993), quark-gluon plasma (Gervino et al 2012), etc. Ghosh et al (2013) studied the IA GSs in e-p-i plasma composed of nonextensive distributed electrons and positrons, and inertial ions. El-Awady and Moslem (2011) investigated the formation of solitary and rogue waves in the nonextensive e-p-i plasmas and pointed out that the growth or damping of the rogue wave depends on the value of the q-nonextensive parameter.…”

Assumptions and ambiguities in nonplanar acoustic soliton theory

“…We well know that a number of authors have used this assumption in the literature, but unfortunately that does not make it generally correct, at least not without keeping several limitations in mind. Several authors [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] introduce the stretching (4) with a reference to papers by Maxon and Viecelli, 12,13 without mentioning any of the restrictions about its applicability, whereas more often than not other authors do not even advance any motivation whatsoever for its use, as if this were completely selfevident. Because of the fairly large literature on nonplanar waves, we have cited here only a representative selection of those papers addressing electrostatic modes in unmagnetized plasmas, where the description involves only one spatial coordinate, r, without angular dependence.…”

“…However, one finds in the literature other plasma models, which then either lead to an equation like (23), but with more complicated coefficients, [12][13][14][15][16][17][18][19][20][21]24,25,30,32,33,36,[38][39][40][41][42]44,46,49,54 or to modifications of related evolution equations like the Burgers, 23,31,35 KdV-Burgers, 22,37,45,47,48 Gardner, [26][27][28][29]34,43,44,[50][51][52][53]55,56 or Schamel 23 equations. The standard forms of these equations have been well studied in the literature over many decades.…”

“…22,23,28,29,31,35,37,41,42,45,46,53 Another point of criticism is that, beginning again, already with Maxon and Viecelli, 12-14 many authors [16][17][18][19][20][21]30,33,35,36,[38][39][40][41][46][47][48][49]54 present graphs where the initial KdV soliton amplitudes are far too large to be admissible in an iterative scheme like the reductive perturbation analysis, which neglects higher-order nonlinearities and hence requires variables like u 1 to remain significantly smaller than unity in normalized form. Some authors 24,32,37,42,45,55 start with reasonable values for the undisturbed solution of the planar case, but let these evolve to values of ksk that are too small, so that the amplitudes then exceed allowable limits.…”

Comment on “Nonplanar dust-ion acoustic Gardner solitons in a dusty plasma with q-nonextensive electron velocity distribution” [Phys. Plasmas 19, 033703 (2012)]

“…In reality, this solution is the double layer (DL) solution that has been shown in some recently published articles. [3][4][5][6][7][8][9] In fact, the GSs solution is completely different from their solution and has been studied by several authors 2,[6][7][8][9][10][11] We would like to point out the fact that both Gardner SWs and DLs are the solutions of the standard Gardner (sG) equation, which has been described elaborately in Refs. 2 and 3.…”