  Observations of magnetohydrodynamic (MHD) waves in the structured solar
atmosphere have shown that these waves are damped and can thus contribute to
atmospheric heating. In this paper, we focus on the damping mechanism of
resonant absorption in the cusp continuum. This process takes places when waves
travel through an inhomogeneous plasma. Our aim is to determine the properties
of MHD waves undergoing resonant absorption in the cusp continuum in the
transition layer of a cylindrical solar atmospheric structure, such as a
photospheric pore or a coronal loop. Depending on which quantities dominate,
one can assess what type of classical MHD wave the modes in question resemble
most. In order to study the properties of these waves, we analytically
determine the spatial profiles of compression, displacement, and vorticity for
waves with frequencies in the cusp continuum, which undergo resonant
absorption. We confirm these analytical derivations via numerical calculations
of the profiles in the resistive MHD framework. We show that the dominant
quantities for the modes in the cusp continuum are the displacement parallel to
the background magnetic field and the vorticity component in the azimuthal
direction (i.e. perpendicular to the background magnetic field and along the
loop boundary).
