Two remarks on a generalized Davey–Stewartson system

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...

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Bibliographic Details
Published in:Nonlinear analysis 2006-03, Vol.64 (5), p.979-986
Main Authors: Eden, A., Erbay, H.A., Muslu, G.M.
Format: Article
Language:English
Subjects:
[formula omitted]-stability
Blow-up profile
Davey–Stewartson system
Exact sciences and technology
Mathematical analysis
Mathematics
Nonlinear Schrödinger equation
Partial differential equations
Pseudo-conformal invariance
Sciences and techniques of general use
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Summary: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 < ∞ .
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.05.052