Analytic smoothing effect and global existence for elliptic hyperbolic Davey-Stewartson system

We study the elliptic-hyperbolic Davey-Stewartson equation which is considered as a nonlocal nonlinear Schrodinger equation with nonlinearities involving derivatives of unknown function in two space dimensions. We show that solutions become analytic for any t/spl ne/0 with respect to x if the data are small and decay exponentially when |x|/spl rarr//spl infin/.