On the nonlinear Schrödinger equations of derivative type

Research output: Contribution to journalArticle

85 Citations (Scopus)

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 languageEnglish
Pages (from-to)137-163
Number of pages27
JournalIndiana University Mathematics Journal
Volume45
Issue number1
Publication statusPublished - 1996 Mar
Externally publishedYes

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Cauchy Problem
Nonlinear Equations
Derivative
Wave Operator
Global Well-posedness
Gauge Transformation
System of equations
Infinity
Sufficient Conditions
Energy
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Indiana University Mathematics Journal, Vol. 45, No. 1, 03.1996, p. 137-163.

Research output: Contribution to journalArticle

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