Variable dust charge generates a special type of nonlinear structures through modified Gardner equations

Abstract

Nonlinear damped modified Gardner equation is derived from the dust hydrodynamic model in dusty plasma, which is collisional, unmagnetized, and has two temperature ions. An extended version of the reductive perturbation technique (RPT) is used to derive the said equations. Approximate analytical solitary wave solution is obtained for compositional parameters near the critical composition. It is found that various nonlinear structures like super periodic, superhomoclinic, and special types of nonlinear structures are emerging while an investigation is done through the system of first‐order differential equations. The effects of different plasma parameters like collisions and dust charge variables on the wave structures have been noticed. In the circumstances of nebulas, interstellar clouds, planetary magnetospheres, and cometary environments recognized by astrophysicists, Voyager spacecraft observation on the fine structure of Saturn's rings, semiconductor devices, it has been investigated that the dust charge variable modifies the super nonlinear structures significantly.