We investigate the interaction of a plane , linearly polarized , Alfvénic pulse with a one-dimensional , perpendicular to the magnetic field , plasma density inhomogeneity in the strongly nonlinear regime . Our numerical study of the full MHD equations shows that : ( i ) Plasma density inhomogeneity substantially enhances ( by about a factor of 2 ) the generation of longitudinal compressive waves . ( ii ) Attained maximal values of the generated transverse compressive perturbations are insensitive to the strength of the plasma density inhomogeneity , plasma \beta and the initial amplitude of the Alfvén wave . Typically , they reach about 40 % of the initial Alfvén wave amplitude . ( iii ) Attained maximal values of the generated relative density perturbations are within 20-40 % for 0.5 \leq \beta \leq 2.0 . They depend upon plasma \beta strongly ; and scale almost linearly with the initial Alfvén wave amplitude .