## Abstract

We study the elliptic-hyperbolic Davey-Stewartson system , where c1, c2 ∈ R, u is a complex valued function and φ is a real valued function. The system can be translated to nonlocal nonlinear Schrödinger equations after a rotation and a rescaling, where c0, c1, c2 ∈ C. Our purpose in this paper is to prove that if the norm ||(π^{2}_{j=1} cosh θx_{j})u0||3,0 + ||(π^{2}_{j=1} cosh θx_{j})u0||0,3 for θ ≠ 0 is sufficiently small, then small solutions of (NLS) exist and become analytic with respect to x for any t ≠ 0 . Here we denote the weighted Sobolev space by H^{m,s} = {φ ∈ L^{2}; ||φ||_{m,s} =(1+x^{2}_{1}+x^{2}_{2})^{s/2}(1-∂^{2}_{x1}-∂^{2}_{x2})^{m/2}φ|| < infin; }, m, s ∈ R^{+}.

Original language | English |
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Pages (from-to) | 469-492 |

Number of pages | 24 |

Journal | Advances in Differential Equations |

Volume | 7 |

Issue number | 4 |

Publication status | Published - 2002 Dec 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics