Reflection and dissipation of Alfv\'en waves in interstellar clouds
  Context: Supersonic nonthermal motions in molecular clouds are often
interpreted as long-lived magnetohydrodynamic (MHD) waves. The propagation and
amplitude of these waves is affected by local physical characteristics, most
importantly the gas density and the ionization fraction.
  Aims: We study the propagation, reflection and dissipation of Alfv\'en waves
in molecular clouds deriving the behavior of observable quantities such as the
amplitudes of velocity fluctuations and the rate of energy dissipation.
  Methods: We formulated the problem in terms of Els\"asser variables for
transverse MHD waves propagating in a one-dimensional inhomogeneous medium,
including the dissipation due to collisions between ions and neutrals and to a
nonlinear turbulent cascade treated in a phenomenological way. We considered
both steady-state and time-dependent situations and solved the equations of the
problem numerically with an iterative method and a Lax-Wendroff scheme,
respectively.
  Results: Alfv\'en waves incident on overdense regions with density profiles
typical of cloud cores embedded in a diffuse gas suffer enhanced reflection in
the regions of the steepest density gradient, and strong dissipation in the
core's interior. These effects are especially significant when the wavelength
is intermediate between the critical wavelength for propagation and the typical
scale of the density gradient. For larger wave amplitudes and/or steeper input
spectra, the effects of the perpendicular turbulent cascade result in a
stronger energy dissipation in the regions immediately surrounding the dense
core.
  Conclusions: The results may help to interpret the sharp decrease of line
width observed in the environments of low-mass cloud cores in several molecular
transitions.
