Study of Breather Structures in the Framework of Gardner Equation in Electron-Positron-Ion Plasmas

TL;DR

This paper investigates breather soliton structures in a complex electron-positron-ion plasma using analytical and numerical methods, revealing the existence and behavior of these localized oscillating waves with potential applications in space and laboratory plasmas.

Contribution

It introduces a novel analysis of breather solutions in Gardner equation within a multi-component plasma system, combining reductive perturbation and Hirota methods with numerical simulations.

Findings

Breather solutions exist in the studied plasma system.

Superthermal electrons and positrons influence soliton structures.

Numerical simulations confirm analytical results.

Abstract

In different nonlinear mediums, the wave trains carry energy and expose many amazing features. To describe a nonlinear phenomenon, a soliton is one that preserves its shape and amplitude even after the collision. Breather is one kind of soliton structure, which is a localized wave that periodically oscillates in amplitude. This article uses the reductive perturbation technique (RPT) to get the GE from a plasma system with four parts: cold positrons that can move, hot positrons and hot electrons that are spread out in a kappa pattern, and positive ions that can't move. Then, using the Hirota bilinear method (HBM), it is possible to obtain the multi-soliton and breather structures of GE. Breathers are fluctuating regional wave packets and significantly participate in hydrodynamics as well as optics; besides, their interaction can alter the dynamical characteristics of the wave fields. We also incorporate a detailed numerical simulation study based on a newly designed code by two of the co-authors. It is found that in our plasma system, soliton solutions, especially breather solutions, exist. Although superthermal (kappa-distributed) electrons and positrons play an important role in soliton structures, This type of analysis can also apply to the propagation of finite-amplitude waves in natural phenomena like the atmosphere, ocean, optic fibres, signal processing, etc. It should also be useful to study different electrostatic disturbances in space and laboratory plasmas, where immobile positive ions, superthermal electrons, superthermal hot positrons, and mobile cold positrons are the major plasma species.