Two remarks on a generalized Davey-Stewartson system
Eden, Osman Alp
Erbay, Hüsnü Ata
Muslu, Gülçin Mihriye
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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.