Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146996 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II / H. Yamane // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146996 |
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Yamane, H. 2019-02-12T18:09:40Z 2019-02-12T18:09:40Z 2015 Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II / H. Yamane // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q55; 35Q15 DOI:10.3842/SIGMA.2015.020 https://nasplib.isofts.kiev.ua/handle/123456789/146996 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. This work was partially supported by JSPS KAKENHI Grant Number 26400127. Parts of this work were done during the author’s stay at Wuhan University. He wishes to thank Xiaofang Zhou for helpful comments and hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II |
| spellingShingle |
Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II Yamane, H. |
| title_short |
Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II |
| title_full |
Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II |
| title_fullStr |
Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II |
| title_full_unstemmed |
Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II |
| title_sort |
long-time asymptotics for the defocusing integrable discrete nonlinear schrödinger equation ii |
| author |
Yamane, H. |
| author_facet |
Yamane, H. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146996 |
| citation_txt |
Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II / H. Yamane // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. |
| work_keys_str_mv |
AT yamaneh longtimeasymptoticsforthedefocusingintegrablediscretenonlinearschrodingerequationii |
| first_indexed |
2025-12-07T13:37:49Z |
| last_indexed |
2025-12-07T13:37:49Z |
| _version_ |
1850856880221454336 |