NONELLIPTIC SCHRODINGER-EQUATIONS

Nonelliptic Schrodinger equations are defined as multidimensional nonl inear dispersive wave equations whose linear part in the space variabl es is not an elliptic equation. These equations arise in a natural fas hion in several contexts in physics and fluid mechanics. The aim of th is paper is twofold. First, a brief survey is made of the main nonelli ptic Schrodinger equations known by the authors, with emphasis on wate r waves. Second. a theory is developed for the Cauchy problem for sele cted examples. The method is based on linear estimates which are stron gly related to the dispersion relation of the problem.