We study the initial value problem for the elliptic-hyperbolic Davey-Stewartson systems (equation presented) where Δ = ∂2x1 + ∂2x2, c1, C2 ∈ R, u is a complex valued function and φ is a real valued function. When (c1,c2) = (-1,2) the system (*) is called DSI equation in the inverse scattering literature. Our purpose in this paper is to prove the local existence of a unique solution to (*) in the Sobolev space H2(R2) without the smallness condition on the data which were assumed in previous works , , , . Our result is a positive answer to Question 7 in .
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