Proceedings of the Japan Academy, Series A, Mathematical Sciences

Remarks on global behavior of solutions to nonlinear Schrödinger equations

Sunagawa Hideaki and Kawahara Yuichiro

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Abstract

We consider the initial value problem for systems of cubic nonlinear Schrödinger equations in one space dimension with small initial data. We present a structural condition on the nonlinearity under which the solution exists globally in time and behaves like a free solution at infinity. This condition corresponds to an NLS version of the \emph{null condition}.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 82, Number 8 (2006), 117-122.

Dates
First available in Project Euclid: 6 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1162820090

Digital Object Identifier
doi:10.3792/pjaa.82.117

Mathematical Reviews number (MathSciNet)
MR2279276

Zentralblatt MATH identifier
1119.35091

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions

Keywords
Nonlinear Schr\"odinger equations global existence asymptotic behavior null condition

Citation

Yuichiro, Kawahara; Hideaki, Sunagawa. Remarks on global behavior of solutions to nonlinear Schrödinger equations. Proc. Japan Acad. Ser. A Math. Sci. 82 (2006), no. 8, 117--122. doi:10.3792/pjaa.82.117. https://projecteuclid.org/euclid.pja/1162820090


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