| 一类分段光滑临界半线性奇摄动微分方程的空间对照结构解 |
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| 引用本文： | LIUBAVIN Aleksei,倪明康,吴潇.一类分段光滑临界半线性奇摄动微分方程的空间对照结构解[J].吉林大学学报(理学版),2021,58(6):1303-1309. |
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| 作者姓名： | LIUBAVIN Aleksei 倪明康 吴潇 |
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| 作者单位： | 1. 华东师范大学 数学科学学院, 上海 200062;
2. 上海市核心数学与实践重点实验室, 上海 200062 |
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| 摘 要： | 考虑一类具有临界情形的分段光滑奇摄动常微分方程边值问题, 先用边界层函数法和光滑缝接法构造具有内部层和边界层解的渐近展开式, 然后用介值定理证明该问题解的存在性并给出所构造渐近展开式的精度.
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| 关 键 词： | 空间对照结构 渐近展开 边界层函数法 光滑缝接法 奇异摄动理论 |
| 收稿时间： | 2021-05-18 |
Soliton Solutions of a Class of Discrete Integrable Systems |
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| LIUBAVIN Aleksei,NI Mingkang,WU Xiao.Soliton Solutions of a Class of Discrete Integrable Systems[J].Journal of Jilin University: Sci Ed,2021,58(6):1303-1309. |
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| Authors: | LIUBAVIN Aleksei NI Mingkang WU Xiao |
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| Institution: | 1. School of Mathematical Sciences, East China Normal University, Shanghai 200062, China;
2. Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200062, China
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| Abstract: | By using Darboux transformation method, we discussed a class of discrete integrable systems. Starting from a new initial solution, the exact solutions of the equation were given by using Darboux transformation, and then the 1-bell-shaped soliton solution, 1-kink-shaped soliton solution, 2-anti-bell-shaped soliton solution and periodic solutions of the equation were given by choosing the appropriate parameters, and the images of these solutions were given. We analyzed their structures, elastic and inelastic collisions of these solutions through these images. |
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| Keywords: | discrete integrable system Darboux transformation method soliton solution |
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