We numerically and theoretically investigated the completely localized solitons, obtained by the Petviashvili method, and their dynamical stabilities in a magnetized dusty plasma with trapped ions. The results suggest that its amplitudes are proportional to the square of its speed and inversely proportional to the square of the nonlinear interaction strength, which are also confirmed analytically. The dependence of the soliton amplitudes on various physical parameters is investigated systematically. Numerical results indicate that the localized solitons are always dynamically stable. When two localized solitons collide, their amplitudes and phase are nearly invariant. However, if a stable localized soliton collides with an unstable line soliton, the latter will evolve into a series of completely localized solitons.
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