Head-on collision of ion-acoustic (modified) Korteweg–de Vries solitons in Saturn's magnetosphere plasmas with two temperature superthermal electrons

Abstract

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.

A novel analytical technique for analyzing the (3+1)-dimensional fractional calogero- bogoyavlenskii-schiff equation: investigating solitary/shock waves and many others physical phenomena

“…In future work, we can apply the proposed method to study and analyze many evolution equations that are used to describe the characteristics of many nonlinear phenomena that arise in different plasma systems. For example, it is possible to study the effect of the time and space fractional parameters on the properties of solitary and shock waves that arise within the various plasma systems, which are described by the Korteweg-de Vries (KdV)-type equations with third-order dispersion (e.g., KdV, modified KdV (mKdV), Extended/Gardner KdV equation, KdV-Burgers equation, and so on) [41][42][43][44][45][46][47][48][49][50][51][52] and higher-order dispersion (e.g., Kawahara-type equation with some physical effects) and many other related equations [53][54][55][56][57][58][59][60][61][62][63][64], whether in their integral or nonintegral form. Also, this method can be applied to investigating modulated nonlinear structures such as modulated envelope solitons, modulated cnoidal waves, rogue waves and breathers that are described by the standard form of undamped planar nonlinear Schrödinger equation (NLSE) [65][66][67][68][69][70][71][72][73][74] and the damped or nonplanar NLSE [75][76][77][78][79]…”