Complex Korteweg-de Vries equation and nonlinear dust-acoustic waves in a magnetoplasma with a pair of trapped ions

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 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 ions.