We conduct hybrid numerical simulations with particle protons and fluid electrons of a low-frequency, planar (body) and shear Alfv¿n wave imbedded in a smoothly varying cross-field pressure-balanced structure which provides a wave-speed gradient. We consider wave propagation directions starting at 90¿, which resembles the case of a surface wave, and less than 90¿ with respect to the gradient direction. We find that the planar Alfv¿n wave undergoes resonant absorption. When the propagation direction is less than 90¿, we show that there are resonant field lines which can actually lose wave energy to other neighboring resonant field lines, which is a situation that has not been encountered in previous work with surface waves. A consequence of this process is an overall faster development time for smaller scales perpendicular to the magnetic field through phase mixing and potentially faster dissipation of these generated scales in coronal and solar wind plasma.