Interaction of Gardner solitons in plasmas: applications in the Saturn’s magnetosphere

Abstract

Multi-soliton solutions of the Gardner equation (GE) have been obtained using the Hirota’s bilinear formalism and, to the best of our knowledge, have been studied in the context of plasmas for the first time. The results have been used to study the electrostatic waves on the ion time scale in a two-electron temperature (TET) kappa distributed plasma in the light of the data obtained from Saturn’s Magnetosphere. The most important result that has come out of the investigation of multi-soliton solution of GE is that both overtaking and head on interactions may occur owing to the simultaneous presence of quadratic and cubic nonlinearities in the GE. The plasma parameters of the system have been found to influence the spatial scale of interaction. The results of kappa distributed plasma have been compared with the Maxwellian case and the key differences with regard to the parametric regimes for the existence of ion acoustic Gardner solitons and the soliton interaction for the two cases have also been explored in detail.

Soliton collisions in spin–orbit coupled spin-1 Bose–Einstein condensates

“…Solitons exist universally in the natural world due to their remarkable stability and particlelike properties, and have been extensively investigated in a variety of physical systems, such as fibre optics [1,2], field theory [3,4], Bose-Einstein condensate (BEC) [5][6][7], plasmas [8][9][10], acoustics [11], magnetic system [12][13][14], nematic liquid crystals [15], ocean waves [16], and have been observed in many other diverse phenomena, even in the collective oscillations of protein and DNA molecules, and Boson stars. In the studies of ultracold atomic gases, matter-wave solitons play the roles of the fundamental collective-excitation modes, the study of matter-wave solitons becomes one of the most rapidly developing themes in atomic BEC, and has received great attention [17][18][19][20][21].…”

Study of Fuzzy Fractional Third-Order Dispersive KdV Equation in a Plasma under Atangana-Baleanu Derivative

“…Moreover, the head-on collisions between the two-counterpart KdV and modified KdV (mKdV) planar solitons were investigated in different plasma models [52][53][54]. In addition to, the planar and nonplanar Gardner equations were used for modeling the several types of acoustic waves (AWs) in different plasma models [55][56][57][58]. All the abovementioned equations succeeded in giving a good description to many nonlinear phenomena that arise and propagate within different plasma systems and many other branches of science.…”

Interaction of electron acoustic solitons in auroral region for an electron beam plasma system

“…Lately, the critical point has also been taken care of and in such a case one obtains Gardner equation which involves both the quadratic and cubic nonlinearities. Many researchers have explored these equations and their versions in the higher dimensions in the recent past (Mannan and Mamun, 2011;Masud et al, 2012;Abdikian et al, 2020;Nawaz et al, 2021;Nawaz et al, 2022).…”

“…In Hirota's formalism, the transformations are used in terms of dependent variable functions for which the perturbation expansions truncate the higher orders to obtain the multisoliton solutions. Multi-soliton solutions of Korteweg-de Vries (KdV) (Jahangir et al, 2015;Jahangir and Masood, 2020), Kadomtsev Petviashvili (KP) equation (Jahangir et al, 2016), Zakharov Kuznetsov (ZK) equation (Yousaf Khattak et al, 2021) and their variants (Verheest and Hereman, 2019;Nawaz et al, 2021;Nawaz et al, 2022) have been studied in magnetized and unmagnetized plasmas using Hirota's method.…”