On the Davey-Stewartson systems

Abstract We study the initial value problem for the Davey-Stewartson systems. This model arises generically in both physics and mathematics. Using the classification in [15] we consider the elliptic-hyperbolic and hyperbolic-hyperbolic cases. Under smallness assumption on the data it is shown that the IVP is locally wellposed in weighted Sobolev spaces.

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