Analytical solution of dust acoustic waves governed by the damped KdV equation in inhomogeneous nonthermal plasmas

The linear and nonlinear propagation of dust–acoustic waves in an inhomogeneous dusty plasma with nonthermal electrons and ions is investigated. The effects of electron and ion nonthermality, equilibrium plasma densities, dust charge, and temperature ratio are included. By applying the reductive perturbation method, we derive a damped Korteweg–de Vries equation governing the nonlinear evolution of the dust-acoustic mode. The resulting equation and its analytical solution are examined in detail. The soliton amplitude exhibits a non-monotonic dependence on the nonthermal parameters, attaining a maximum at intermediate values as a result of the competition between nonlinearity and dispersion. The results emphasize the joint influence of plasma inhomogeneity, nonthermal populations, and dust charging on dust–acoustic wave dynamics, and they may be tested against contemporary experimental observations in complex plasmas. In several limiting cases, the present results reduce to previously reported models, and the findings are applicable to both laboratory and space dusty plasma studies.