  The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty
plasma with a pair of trapped ions is investigated. Starting from a set of
hydrodynamic equations for massive dust fluids as well as kinetic Vlasov
equations for ions, and applying the reductive perturbation technique, a
Korteweg-de Vries (KdV)-like equation with a complex coefficient of
nonlinearity is derived, which governs the evolution of small-amplitude DA
waves in plasmas. The complex coefficient arises due to vortex-like
distributions of both positive and negative ions. An analytical as well as
numerical solution of the KdV equation are obtained and analyzed with the
effects of external magnetic field, the dust pressure as well as different mass
and temperatures of positive and negative ions.
