The analysis of nonlinear wave equations has experienced a dramatic growth in
the last ten years or so. The key factor in this has been the transition from
linear analysis, first to the study of bilinear and multilinear wave
interactions, useful in the analysis of semilinear equations, and next to the
study of nonlinear wave interactions, arising in fully nonlinear equations. The
dispersion phenomena plays a crucial role in these problems. The purpose of
this article is to highlight a few recent ideas and results, as well as to
present some open problems and possible future directions in this field
