[en] The problem of spatial depletion of propagating lower-hybrid waves in an inhomogeneous plasma is investigated, and in particular, the nonlinear evolution of a lower-hybrid pump which is coupled to a daughter lower-hybrid decay wave excited by low-frequency density perturbations. The results show that pump depletion occurs when three-dimensional effects are included. This phenomenon competes with the filamentation of the pump caused by self-interaction. Implications to lower-hybrid heating experiments are discussed. (author)