Study of multi-solitons, breather structures in dusty plasma with generalized polarization force

Abstract

A theoretical inquiry delves into the presence of multiple solitons and breather configurations within a nonuniform, inhomogeneous, unmagnetized dusty plasma characterized by universally polarized force. This system encompasses ions, electrons, positively and negatively charged dust particles, distributed in accordance with a superthermal distribution. Employing the reductive perturbation technique (RPT), the Gardner equation (GE) is derived from the fundamental hydrodynamical model equations. The multi-solitons of the GE are synthesized utilizing the Hirota bilinear method (HBM), which further facilitates the exploration of breather solutions via the appropriate selection of complex wave numbers. The system exhibits both compressive and rarefactive multi-solitons. Moreover, the behavior of breather structures varies depending on associated plasma parameters; occasionally, they overlap, while at other times, they remain entirely disjoint. This research holds relevance for investigating the propagation of finite-amplitude waves in natural phenomena such as the atmosphere, oceans, optic fibers, and signal processing.

Figures display the interaction between two-solitons (a), and breather structures (b), of the Gardner equation in dusty plasma with polarized force for the parameter values \(k_i = 5, k_e = 2.5, \mu _i = 0.7, \mu _e = 0.3, \mu = 10, \rho = 1.01, \sigma _i = 0.1, R = 0.5, Z = 0.01\), respectively. The manuscript presents some graphs to illustrate the propagation and interaction between two-soliton solutions, as well as the propagation of various breather structures in dusty plasma under polarized force. We explore the presented wave solutions using the symbolic computation software Mathematica. The diversity in two-solitons and breather structures depends on the plasma parameter and the choice of wave number, real or complex. This work analyzes, through graphical representation, how the plasma system affects the above nonlinear structures.