The nonlinear propagation of small but finite amplitude dust-ion-acoustic solitary waves in a magnetized, collisionless dusty plasma is investigated theoretically. It has been assumed that the electrons are trapped following the vortex-like distribution and that the negatively and positively charged ions are mobile with the presence of charge fluctuating stationary dusts, where ions mass provide the inertia and restoring forces are provided by the thermal pressure of hot electrons. A reductive perturbation method was employed to obtain a modified Korteweg-de Vries (mK-dV) equation for the first-order potential and a stationary solution is obtained. The effect of the presence of trapped electrons, negatively and positively charged ions and arbitrary charged dust grains are discussed.
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