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Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data

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Abstract

We study the initial value problem for the elliptic-hyperbolic Davey-Stewartson systems {ie133-01} where {ie133-2},u is a complex valued function and φ is a real valued function. When (c 1,c 2) = (-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 spaceH 2(R 2) without the smallness condition on the data which were assumed in previous works [7], [17], [19], [26], Our result is a positive answer to Question 7 in [24].

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  1. Department of Applied Mathematics, Science University of Tokyo, 1-3, Kagurazaka, Shinjuku-ku, 162, Tokyo, Japan

    Nakao Hayashi

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  1. Nakao Hayashi
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Hayashi, N. Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data. J. Anal. Math. 73, 133–164 (1997). https://doi.org/10.1007/BF02788141

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  • DOI: https://doi.org/10.1007/BF02788141

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