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Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II
Інший ID:
2010 Mathematics Subject Classification: 35Q55; 35Q15
DOI:10.3842/SIGMA.2015.020
DOI:10.3842/SIGMA.2015.020
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
567
Завантажень:
270
Анотація:
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.
