Study of nonlinear waves structures through damped modified Gardner equations in quantum plasmas

The multicomponent quantum hydrodynamic model of collisional, unmagnetized electron-ion-dust quantum plasma has been considered to derive the nonlinear damped modified Gardner equations. For compositional values close to the critical composition, damped modified Gardner equations are formulated using an expanded version of the reductive perturbation technique. It is found that this electron-ion-dust quantum plasma provides the required critical composition. It is possible to construct a new approximate analytical solitary wave solution, which appears to have novel nonlinear properties incorporated in it. Through a recently found approximate analytical solution, the impact of dust ion and quantum diffraction parameter collision on solitary wave structures is investigated. It can be seen that the structures of solitary wave solutions are distinctively modified by dust ion collision and the quantum diffraction parameter. The crucial role of collision parameter and the quantum diffraction parameter on the solitary wave structures has been studied extensively.