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On the Davey-Stewartson systems. (English) Zbl 0807.35136
The main purpose is to establish local well-posedness results for the initial value problem of the Davey-Stewartson systems for small data. To this end, the initial IVP problem is converted into another one corresponding to the elliptic-hyperbolic case or the hyperbolic- hyperbolic one depending upon the value of its structural parameter. It is shown that the IVP is locally well posed in weighted Sobolev spaces. Linear estimates, and then nonlinear estimates are obtained, which are then utilized for the proof of the main results.

MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35E15Initial value problems of PDE with constant coefficients
35D05Existence of generalized solutions of PDE (MSC2000)