Two remarks on a generalized Davey-Stewartson system


Eden A., ERBAY H., Muslu G. M.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.64, no.5, pp.979-986, 2006 (SCI-Expanded) identifier identifier

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 < infinity. (c) 2005 Elsevier Ltd. All rights reserved.