Hokkaido Mathematical Journal
- Hokkaido Math. J.
- Volume 30, Number 2 (2001), 451-473.
Global existence for a class of cubic nonlinear Schrödinger equations in one space dimension
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).
Hokkaido Math. J., Volume 30, Number 2 (2001), 451-473.
First available in Project Euclid: 22 October 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions
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