Two remarks on a generalized Davey–Stewartson system

Abstract

We present two results on a generalized Davey–Stewartson system, both following from the pseudo-conformal invariance of its solutions. In the hyperbolic–elliptic–elliptic case, under some conditions on the physical parameters, we establish a blow-up profile. These conditions turn out to be necessary conditions for the existence of a special “radial” solution. In the elliptic–elliptic–elliptic case, under milder conditions, we show the L p -norms of the solutions decay to zero algebraically in time for 2 < p < ∞ .