### 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∥

Original language | English |
---|---|

Pages (from-to) | 453-461 |

Number of pages | 9 |

Journal | Differential and Integral Equations |

Volume | 7 |

Issue number | 2 |

Publication status | Published - 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Differential and Integral Equations*,

*7*(2), 453-461.

**Remarks on nonlinear Schrödinger equations in one space dimension.** / Hayashi, Nakao; Ozawa, Tohru; Bona, J. L.

Research output: Contribution to journal › Article

*Differential and Integral Equations*, vol. 7, no. 2, pp. 453-461.

}

TY - JOUR

T1 - Remarks on nonlinear Schrödinger equations in one space dimension

AU - Hayashi, Nakao

AU - Ozawa, Tohru

AU - Bona, J. L.

PY - 1994

Y1 - 1994

N2 - We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥

AB - We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥

UR - http://www.scopus.com/inward/record.url?scp=84972525950&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972525950&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972525950

VL - 7

SP - 453

EP - 461

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 2

ER -