  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.
