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 SIGMA, 2015, Volume 11, 020, 17 pages (Mi sigma1001)

Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II

Hideshi Yamane

Department of Mathematical Sciences, Kwansei Gakuin University, Gakuen 2-1 Sanda, Hyogo 669-1337, Japan

Abstract: We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation. If $|n|<2t$, we have decaying oscillation of order $O(t^{-1/2})$ as was proved in our previous paper. Near $|n|=2t$, the behavior is decaying oscillation of order $O(t^{-1/3})$ and the coefficient of the leading term is expressed by the Painlevé II function. In $|n|>2t$, the solution decays more rapidly than any negative power of $n$.

Keywords: discrete nonlinear Schrödinger equation; nonlinear steepest descent; Painlevé equation.

DOI: https://doi.org/10.3842/SIGMA.2015.020

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ArXiv: 1407.5751
MSC: 35Q55; 35Q15
Received: September 6, 2014; in final form March 3, 2015; Published online March 8, 2015
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Citation: Hideshi Yamane, “Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II”, SIGMA, 11 (2015), 020, 17 pp.

Citation in format AMSBIB
\Bibitem{Yam15} \by Hideshi~Yamane \paper Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schr\"odinger Equation~II \jour SIGMA \yr 2015 \vol 11 \papernumber 020 \totalpages 17 \mathnet{http://mi.mathnet.ru/sigma1001} \crossref{https://doi.org/10.3842/SIGMA.2015.020} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3322338} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000350562300001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924374194} 

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This publication is cited in the following articles:
1. Yamane H., “Riemann-Hilbert Factorization of Matrices Invariant Under Inversion in a Circle”, Proc. Amer. Math. Soc., 147:5 (2019), 2147–2157
2. Yamane H., “Long-Time Asymptotics For the Integrable Discrete Nonlinear Schrodinger Equation: the Focusing Case”, Funkc. Ekvacioj-Ser. Int., 62:2 (2019), 227–253
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