Journal of the Mathematical Society of Japan

Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation

Hideshi YAMANE

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Abstract

We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation of Ablowitz-Ladik by means of the inverse scattering transform and the Deift-Zhou nonlinear steepest descent method. The leading part is a sum of two terms that oscillate with decay of order $t^{-1/2}$.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 3 (2014), 765-803.

Dates
First available in Project Euclid: 24 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1406206972

Digital Object Identifier
doi:10.2969/jmsj/06630765

Mathematical Reviews number (MathSciNet)
MR3238317

Zentralblatt MATH identifier
1309.35147

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35Q15: Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]

Keywords
discrete nonlinear Schrödinger equation Ablowitz-Ladik model asymptotics inverse scattering transform nonlinear steepest descent

Citation

YAMANE, Hideshi. Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation. J. Math. Soc. Japan 66 (2014), no. 3, 765--803. doi:10.2969/jmsj/06630765. https://projecteuclid.org/euclid.jmsj/1406206972


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References

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