[1]张文娴,邓圣福.离散非线性薛定谔方程的1∶1共振[J].华侨大学学报(自然科学版),2023,44(4):526-532.[doi:10.11830/ISSN.1000-5013.202204026]
　ZHANG Wenxian,DENG Shengfu.1∶1 Resonance of Discrete Nonlinear Schr?dinger Equation[J].Journal of Huaqiao University(Natural Science),2023,44(4):526-532.[doi:10.11830/ISSN.1000-5013.202204026]
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离散非线性薛定谔方程的1∶1共振()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第44卷
期数:
2023年第4期
页码:
526-532
栏目:
出版日期:
2023-07-17

文章信息/Info

Title:
1∶1 Resonance of Discrete Nonlinear Schr?dinger Equation
文章编号:
1000-5013(2023)04-0526-07
作者:
张文娴;  邓圣福
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
ZHANG Wenxian;  DENG Shengfu
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
离散非线性薛定谔方程;  差分系统;  1∶1共振;  Picard迭代;  退化平衡点;  多项式函数
Keywords:
discrete nonlinear Schr? dinger equation;  difference system;  1∶1 resonance;  Picard iteration;  degenerate equilibrium;  polynomial function
分类号:
O175.1
DOI:
10.11830/ISSN.1000-5013.202204026
文献标志码:
A
摘要:
为研究离散非线性薛定谔方程在不动点附近的1∶1共振问题,将离散非线性薛定谔方程化为差分系统,差分系统线性算子的特征值为两重根1;然后,利用Picard迭代及时间1映射,将差分系统转换为常微分系统,推导差分系统不动点的稳定性;最后,用数学软件模拟差分系统的局部相图.研究结果表明:不动点是局部渐近稳定的.
Abstract:
In order to study 1∶1 resonance problem of discrete nonlinear Schr?dinger equation near the fixed point, firstly, this discrete nonlinear Schr?dinger equation is transformed into a difference system, the eigenvalue of the difference system linear operator is double root 1, and then, by the use of Picard iteration and the time-one map, this difference system is converted into an ordinary differential system, the stability of the fixed point of the difference system is obtained. Lastly, the local phase portraits of the difference system are also simulated by mathematical software. The result shows that the fixed point is locally asymptotically stable.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2022-04-26
通信作者: 邓圣福(1974-),男,教授,博士,主要从事微分方程和动力系统研究.E-mail:sfdeng@hqu.edu.cn.
基金项目: 国家自然科学基金面上资助项目(12171171)
更新日期/Last Update: 2023-07-20