  The deformed relativistic Hartree-Bogoliubov theory in continuum with the
density-dependent meson-nucleon couplings is developed. The formulism is
briefly presented with the emphasis on handling the density-dependent
couplings, meson fields, and potentials in axially deformed system with partial
wave method. Taking the neutron-rich nucleus $^{38}$Mg as an example, the newly
developed code is verified by the spherical relativistic continuum
Hartree-Bogoliubov calculations, where only the spherical components of the
densities are considered. When the deformation is included self-consistently,
it is shown that the spherical components of density-dependent coupling
strengths are dominant, while the contributions from low-order deformed
components are not negligible.
