### Abstract

This paper studies the Cauchy problem both at finite and infinite times for a class of nonlinear Schrödinger equations with coupling of derivative type. The proof uses gauge transformations which reduce the original equations to systems of equations without coupling of derivative type. Concerning the Cauchy problem at finite times, we give sufficient conditions for the global well-posedness in the energy space. Concerning the Cauchy problem at infinity, we construct modified wave operators on small and sufficiently regular asymptotic states.

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

Pages (from-to) | 137-163 |

Number of pages | 27 |

Journal | Indiana University Mathematics Journal |

Volume | 45 |

Issue number | 1 |

Publication status | Published - 1996 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indiana University Mathematics Journal*,

*45*(1), 137-163.

**On the nonlinear Schrödinger equations of derivative type.** / Ozawa, Tohru.

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 45, no. 1, pp. 137-163.

}

TY - JOUR

T1 - On the nonlinear Schrödinger equations of derivative type

AU - Ozawa, Tohru

PY - 1996/3

Y1 - 1996/3

N2 - This paper studies the Cauchy problem both at finite and infinite times for a class of nonlinear Schrödinger equations with coupling of derivative type. The proof uses gauge transformations which reduce the original equations to systems of equations without coupling of derivative type. Concerning the Cauchy problem at finite times, we give sufficient conditions for the global well-posedness in the energy space. Concerning the Cauchy problem at infinity, we construct modified wave operators on small and sufficiently regular asymptotic states.

AB - This paper studies the Cauchy problem both at finite and infinite times for a class of nonlinear Schrödinger equations with coupling of derivative type. The proof uses gauge transformations which reduce the original equations to systems of equations without coupling of derivative type. Concerning the Cauchy problem at finite times, we give sufficient conditions for the global well-posedness in the energy space. Concerning the Cauchy problem at infinity, we construct modified wave operators on small and sufficiently regular asymptotic states.

UR - http://www.scopus.com/inward/record.url?scp=0003001402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003001402&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0003001402

VL - 45

SP - 137

EP - 163

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 1

ER -