  The nonlinear propagation of electrostatic dust-acoustic (DA) waves in a
magnetized dusty plasma consisting of negatively charged mobile dusts,
nonthermal fast electrons and trapped ions with vortex-like distribution is
studied. Using the reductive perturbation technique, a Korteweg-de Vries
(KdV)-like equation is derived which governs the dynamics of the
small-amplitude solitary waves in a magnetized dusty nonthermal plasma. It is
found that due to the dust thermal pressure, there exists a critical value
$(\beta_c)$ of the nothermal parameter $\beta~(>1)$, denoting the percentage of
energetic electrons, below which the DA solitary waves cease to propagate. The
soliton solution (travelling wave) of the KdV-like equation is obtained, and is
shown to be only of the rarefactive type. The properties of the solitons are
analyzed numerically with the system parameters. It is also seen that the
effect of the static magnetic field (which only modifies the soliton width)
becomes significant when the dust gyrofrequency is smaller than one-tenth of
the dust plasma frequency. Furthermore, the amplitude of the soliton is found
to increase (decrease) when the ratio of the free to trapped ion temperatures
$(\sigma)$ is positive (negative). The effects of the system parameters
including the obliqueness of propagation $(l_z)$ and $\sigma$ on the dynamics
of the DA solitons are also discussed numerically, and it is found that the
soliton structures can withstand perturbations and turbulence during a
considerable time. The results should be useful for understanding the nonlinear
propagation of DA solitary waves in laboratory and space plasmas (e.g., Earth's
magnetosphere, auroral region, heliospheric environments etc.).
