### Abstract

We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂_{x} = ∂/∂x and F: C^{4} → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u_{0}, it is shown that (+) has a unique local solution in time if u_{0} is in H^{3, 0} ∩ H^{2, 1}, where H^{m, s} = {f ∈ S’ ∥f∥^{m, s} = ∥(1 + x^{2})^{s/2} (1-Δ)f∥<∞}, m, s ∈ ℝ.

Original language | English |
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Pages (from-to) | 453-461 |

Number of pages | 9 |

Journal | Differential and Integral Equations |

Volume | 7 |

Issue number | 2 |

Publication status | Published - 1994 Mar |

Externally published | Yes |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Hayashi, N., Ozawa, T., & Bona, J. L. (1994). Remarks on nonlinear Schrödinger equations in one space dimension.

*Differential and Integral Equations*,*7*(2), 453-461.