  {\it Ab initio} quantum-mechanical calculations of the differential and
integrated cross sections of the elastic scattering, Stark transitions, and
Coulomb de-excitation at collisions of excited $\mu^- p$ and $\mu^- d$ atoms
with hydrogen isotope atoms in the ground state are performed. The scattering
processes are treated in a unified manner in the framework of the
close-coupling approach. The used basis includes both open and closed channels
corresponding to all exotic atom states with principal quantum numbers from
$n=1$ up to $n_{\rm max}=20$. The energy shifts of $ns$ states due to electron
vacuum polarization and finite nuclear size are taken into account. The
kinetics of atomic cascade of $\mu^- p$ and $\mu^- d$ atoms are studied in a
wide range of relative target densities ($\varphi = 10^{-8} -1$) within the
improved version of the extended cascade model. The results of the numerical
quantum-mechanical calculations of the cross sections for quantum numbers and
kinetic energies of muonic atoms, that are of interest for the detailed cascade
calculations, are used as input data. Initial $(n,l,E)$-distributions of muonic
atoms at the instant of their formation and the target motion are taken into
account explicitly in present cascade calculations. The comparison of the
calculated cross sections, kinetic energy distributions at the instant of the
$np\to 1s$ radiative transitions as well as the absolute and relative $x$-ray
yields for both muonic hydrogen and muonic deuterium reveals the isotopic
effects, which, in principal, may be observed experimentally. The present
results are mainly in very good agreement with experimental data available in
the literature.
