Transmission and reflection of the dust acoustic wave at an interface in an inhomogeneous dusty plasma

Dusty plasmas typically contain various species of dust particles, though most studies have focused on homogeneous systems. This paper investigates the propagation of dust acoustic waves in an inhomogeneous dusty plasma with an interface, analysing how plasma inhomogeneity influences wave behaviour. Using scattering and reductive perturbation methods, we show that both transmitted and reflected waves depend strongly on the mass ratio between regions. Dust acoustic waves cannot propagate through a dust lattice when the wavelength is smaller than the lattice constant. At a discontinuous interface, at least one transmitted solitary wave is generated, with its amplitude determined by the mass ratio, while at most one reflected solitary wave can exist. These results underscore the critical role of the mass ratio in wave propagation and suggest a method for estimating dust particle masses and properties by analysing the incident, transmitted and reflected waves.