Quasi-periodic waves to the defocusing nonlinear Schrödinger equation
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Published:2024-02-02
Issue:3
Volume:37
Page:035010
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ISSN:0951-7715
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Container-title:Nonlinearity
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language:
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Short-container-title:Nonlinearity
Author:
Zhang Ying-NanORCID,
Hu Xing-Biao,
Sun Jian-Qing
Abstract
Abstract
A direct approach for the quasi-periodic wave solutions to the defocusing nonlinear Schrödinger equation is proposed based on the theta functions and Hirota’s bilinear method. We transform the problem into a system of algebraic equations, which can be formulated into a least squares problem and then solved by using numerical iterative methods. A rigorous asymptotic analysis demonstrates that these solutions can be classified into two categories: quasi-periodic oscillatory waves and quasi-periodic dark solitons. Singular behaviors may arise in the former case. The numerical results obtained for both the
(
1
+
1
)
-dimensional and
(
2
+
1
)
-dimensional equations are consistent with the theoretical results. Additionaly, the system of algebraic equations can be further extended to address the Riemann–Schottky problem for hyperelliptic curves with 2 infinite points.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics