2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80894The paper analyses the properties of dusty plasmas in the extreme conditions when the free electrons are absent. The nonlinear Korteveg de Vries equation with a nonlocal (integral) term in a small parameter approximation is derived. The conditions are determined when the integral term is essential hence the Landau damping of two-ion-dusty plasma waves is substantial.Pattern Formation and Solitonstext