In view of the recent observations by plasma science-spacecraft-voyager and Cassini plasma spectrometer of Saturn's magnetosphere, the interaction between two counter-propagating ion-acoustic (IA) solitons is studied in an unmagnetized plasma consisting of warm adiabatic ions in addition to hot and cold electrons following kappa distribution. The head-on collision of the IA solitons is investigated using the extended Poincare–Lighthill–Kuo technique. Since this model supports both compressive and rarefactive solitons, therefore, the soliton collisions for both Korteweg–de Vries (KdV) and the modified KdV (mKdV) equations are investigated. The corresponding phase shifts after the collision for both these equations are also derived and examined. Furthermore, the effects of different plasma parameters (corresponding to Saturn's magnetosphere), including superthermality, density, and temperature on the colliding soliton profiles and their phase shifts, are examined. It is concluded that the phase shift is smaller when both hot and cold electrons are Maxwellian by comparison with the superthermal case.

We have investigated the propagation and interaction of nonlinear electron acoustic waves (EAWs) in a plasma comprising hot (superthermal) and cold electrons and immobile ions. We have derived the Korteweg-de Vries equation for EAWs in the small amplitude limit. Employing the Hirota's Direct method, we have investigated the multisoliton solutions for electron acoustic solitary waves (EASWs). It has been found that the system under consideration admits only rarefactive electrostatic solitary structures. As the observable data are available in terms of electric field rather than electric potential, therefore, we have discussed our results in terms of bipolar electric field structures. The numerical analysis has revealed that the ratio of hot to cold electrons and superthermality of hot electrons play a crucial role in changing the amplitude of EASWs. The interaction of the two solitons and its dependence on the choice of propagation vectors, superthermality, and density ratio have also been elaborated. The results of the present study may be beneficial to comprehend the interaction between two EASWs in astrophysical and laboratory plasmas.

The propagation of electron-acoustic waves (EAWs) in an unmagnetized plasma, comprising $(r,q)$-distributed hot electrons, cold inertial electrons, and stationary positive ions, is investigated. Both the unmodulated and modulated EAWs, such as solitary waves, rogue waves (RWs), and breathers are discussed. The Sagdeev potential approach is employed to determine the existence domain of electron acoustic solitary structures and study the perfectly symmetric planar nonlinear unmodulated structures. Moreover, the nonlinear Schrödinger equation (NLSE) is derived and its modulated solutions, including first order RWs (Peregrine soliton), higher-order RWs (super RWs), and breathers (Akhmediev breathers and Kuznetsov–Ma soliton) are presented. The effects of plasma parameters and, in particular, the effects of spectral indices r and q, of distribution functions on the characteristics of both unmodulated and modulated EAWs, are examined in detail. In a limited cases, the $(r,q)$ distribution is compared with Maxwellian and kappa distributions. The present investigation may be beneficial to comprehend and predict the modulated and unmodulated electron acoustic structures in laboratory and space plasmas.

The properties of ion acoustic solitary and periodic structures are studied in magnetized two-ion component (O⁺ − H⁺ − e) plasmas with (r, q) distributed electrons. It is found that two modes of ion acoustic waves, namely, fast and slow modes, can propagate in such a plasma. The nonlinear Zakharov–Kuznetsov equation is derived using the well-known reductive perturbation method. Employing the theory of planar dynamical systems, the system under consideration is found to admit compressive (hump) and rarefactive (dip) solitary structures and periodic wave solutions. It is found that behavior of propagation of nonlinear ion acoustic solitary structures is different for fast and slow modes owing to the difference in physics of the two modes. The effect of the double spectral indices r and q is thoroughly explored. It is shown that altering the shape of the distribution function through these indices radically alter the propagation characteristics of nonlinear ion acoustic waves. The ratio of concentration of heavy (O⁺) to light ions (H⁺) is found to change the fast mode, whereas the temperature ratio is observed to alter the slow mode. We have applied our study to the upper ionosphere where bi-ion plasmas and the presence of non-Maxwellian electrons have been observed by various satellite missions.

Nonlinear propagation of electrostatic waves with cubic nonlinearity has been investigated in a multicomponent dusty plasma with inertial ions, superthermal two temperature electrons and stationary dust. In this regard, single and multi-soliton solutions of modified Korteweg–de Vries (mKdV) equation for dust ion acoustic waves (DIAWs) have been investigated implementing Hirota’s bilinear method. Plasma parameters affecting the amplitude of dust ion acoustic (DIA) mKdV single soliton have been thoroughly investigated based on the data from Saturn’s magnetosphere. The overtaking interaction of two mKdV solitons has been investigated by changing the percentage of propagation vectors to observe bipolar structure reducing to a single humped structure for a particular value of the ratio of propagation vectors. The most significant outcome of this study has been the investigation of interaction of a compressive and rarefactive dust ion acoustic soliton forming a peculiar composite shape at the interaction point.

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.