Fluctuations in the charges of dust grains, due to capture or liberation of electrons and protons, induce density and momentum losses or gains in dusty plasmas. This mechanism gives rise to wave damping or growth. We address an interesting intermediate regime, where the linear electromagnetic waves are not affected, but the dust charging influences the slower nonlinear development, leading to a derivative nonlinear Schrödinger equation with a source term. As a rule no stable solitary waves are possible, and the damping mechanism still is active.