Solitons collision and freak waves in a plasma with Cairns-Tsallis particle distributions

Abstract

The solitons collision (head-on collision) and rogue waves in an unmagnetized plasma comprising nonthermal-nonextensive distributed (Cairns-Tsallis) electrons and cold ions are investigated. For solitons collision, the extended Poincaré-Lighthill-Kuo (PLK) method is employed to derive the coupled Korteweg-de Vries (KdV) equations and their corresponding phase shifts. It is found that solitons having two polarities can propagate in the present model. The coefficients of the nonlinear terms of the coupled KdV equations vanish at a critical value of nonthermality. Therefore, another set of coupled modified KdV (mKdV) equations with cubic nonlinearity is derived and the corresponding phase shifts are calculated. It is found analytically and numerically that the solutions of the coupled KdV equations allow solitons collision only when the solitons have the same polarity, whereas the coupled mKdV equations allow the collisions between the two solitons of the same and opposite polarities. The influence of the nonthermal-nonextensive parameters on the phase shifts of the solitons collision is examined. Furthermore, the rogue waves are studied in the framework of the mKdV equation. The behavior of the rogue waves is analyzed using the nonlinear Schrödinger equation (NLSE), derived from the mKdV equation. It is found that the rogue wave amplitude shrinks with the increase of the nonextensive parameter. The NLSE derived from the KdV equation cannot support the presence of rogue waves.

On the foundations of statistical mechanics

“…The natural, artificial and social complex systems to which S q and its associated statistical mechanics have been applied are very diverse. They include long-range interacting many-body Hamiltonian systems (see [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] for an overview) of various types and symmetries (let us incidentally mention that long-range versions of the interesting types focused on in [31,32] have not yet been handled), as well as non-Hamiltonian ones [33], low-dimensional dynamical systems [34][35][36][37][38][39][40][41][42][43][44][45][46][47], cold atoms [48][49][50], plasmas [51][52][53][54][55][56][57][58][59], trapped atoms…”

Linear and Nonlinear Electrostatic Excitations and Their Stability in a Nonextensive Anisotropic Magnetoplasma

“…Integrating in the entire velocities, we get the normalized form of electron number density as [39][40][41] n e = [1 + (q − 1)φ] (q+1)/2(q−1) .…”

Polarization force in an opposite polarity dusty plasma with hybrid Cairns–Tsallis distributed electrons

“…The ion acoustic solitary waves have been revisited by William et al [ 36 ] by using the hybrid Cairns–Tsallis velocity distribution for electrons and discussed its range of validity for the existence of acoustic solitons. El‐Tantawy et al [ 37 ] have applied the hybrid distribution function to investigate the head‐on collision of ion acoustic solitons and rogue waves. The study of DAW and dust ion acoustic waves have also been performed with electrons featuring the hybrid Cairns–Tsallis distribution by Saha et al [ 38 ] and Guo and Mei, [ 39 ] respectively.…”