Hokkaido Mathematical Journal

Global existence for a class of cubic nonlinear Schrödinger equations in one space dimension

Satoshi TONEGAWA

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Abstract

In this paper, we prove the global existence of a small solution to the Cauchy problem for the nonlinear Schrödinger equation with a class of cubic nonlinearities in one space dimension. Moreover, we also consider the asymptotic behavior in large time of the solution. Our results says that two cubic nonlinearities given in this paper can be considered as nonlinearities of higher degree (more precisely, of degree 5).

Article information

Source
Hokkaido Math. J., Volume 30, Number 2 (2001), 451-473.

Dates
First available in Project Euclid: 22 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1350911962

Digital Object Identifier
doi:10.14492/hokmj/1350911962

Mathematical Reviews number (MathSciNet)
MR1844828

Zentralblatt MATH identifier
1045.35082

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

Keywords
cubic nonlinear Schrödinger equation asymptotically free solution

Citation

TONEGAWA, Satoshi. Global existence for a class of cubic nonlinear Schrödinger equations in one space dimension. Hokkaido Math. J. 30 (2001), no. 2, 451--473. doi:10.14492/hokmj/1350911962. https://projecteuclid.org/euclid.hokmj/1350911962


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