  We investigate the interaction of magnetohydrodynamic waves with plasma
density inhomogeneities. Our numerical study of the full MHD equations shows
that: (A) Plasma density inhomogeneities are a source of non-linear generation
of transverse compressive waves by a plane Alfven wave, and substantially
enhance (by about a factor of 2) the generation of the longitudinal compressive
waves. (B) Attained maximal values of the generated transverse compressive
waves are insensitive to the strength of the plasma density inhomogeneity and
the initial amplitude of the Alfven wave. (C) Efficiency of the generation
depends weakly upon the plasma beta parameter. The maximum generated amplitude
of transverse compressive wave, up to 32% of the initial Alfven wave amplitude,
is reached for about beta=0.5. The results obtained demonstrate that plasma
inhomogeneities enhance the efficiency of the non-linear wave coupling.
