  We study the oblique propagation of weakly nonlinear dust-ion-acoustic (DIA)
solitary waves (SWs) and shocks in collisional magnetized nonthermal dusty
plasmas that are relevant in laboratory and space (Saturn's E-ring)
environments. We consider plasmas to be composed of $q$-nonextensive hot
electrons, thermal positive ions, and immobile negatively charged dust grains
immersed in a static magnetic field and take into account the effects of ion
creation (source), and ion loss (sink), ion-neutral and ion-dust collisions,
anisotropic ion pressure and dust-charge fluctuations on the evolution of
small-amplitude SWs and shocks. The ion-neutral collision enhancement
equilibrium dust-charge number is self-consistently determined using Newton's
Raphson method. We found that in laboratory dusty plasmas with adiabatic
dust-charge variation [i.e., when the dust charging frequency ($\nu_{\rm{ch}}$)
is much higher than the dust-plasma oscillation frequency
($\omega_{\rm{pd}}$)], the DIA solitary waves (DIASWs) get damped by the
effects of the ion-dust and ion-neutral collisions, whereas the ion creation
and ion loss leads to the amplification of solitary waves, and they appear as
only compressive types with positive potential. On the other hand, in Saturn's
E-ring plasmas, where the collisional and ion creation or ion loss effects are
insignificant, the non-adiabaticity of dust-charge variation can give rise to
the evolution of either damped DIASWs or DIA shocks, depending on the smallness
of the ratios $\nu_{\rm{ch}}/\omega_{\rm{pd}}$ or
$\omega_{\rm{pd}}/\nu_{\rm{ch}}$, respectively. Furthermore, two critical
values of the nonextensive parameter $q$ exist, below (or above) which, the
DIASWs and shocks can appear as rarefactive (or compressive) types. The
characteristics of DIASWs and shocks are also analyzed numerically for
parameters relevant to the laboratory and Saturn's E-ring plasmas.
