Two remarks on a generalized Davey-Stewartson system
MetadataShow full item record
CitationEden, A., Erbay, H. A. & Muslu, G. M. (2006). Two remarks on a generalized Davey–Stewartson system. Nonlinear Analysis, Theory, Methods and Applications, 64(5), 979-986. doi:10.1016/j.na.2005.05.052
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.