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确定有限级数解的阶数上界的一种n阶展开方法

宋宸苇 柳银萍

宋宸苇, 柳银萍. 确定有限级数解的阶数上界的一种n阶展开方法[J]. 华东师范大学学报(自然科学版), 2021, (3): 56-64. doi: 10.3969/j.issn.1000-5641.2021.03.007
引用本文: 宋宸苇, 柳银萍. 确定有限级数解的阶数上界的一种n阶展开方法[J]. 华东师范大学学报(自然科学版), 2021, (3): 56-64. doi: 10.3969/j.issn.1000-5641.2021.03.007
SONG Chenwei, LIU Yinping. An n-order expansion method for determining the upper bound of the order of finite series solutions[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 56-64. doi: 10.3969/j.issn.1000-5641.2021.03.007
Citation: SONG Chenwei, LIU Yinping. An n-order expansion method for determining the upper bound of the order of finite series solutions[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 56-64. doi: 10.3969/j.issn.1000-5641.2021.03.007

确定有限级数解的阶数上界的一种n阶展开方法

doi: 10.3969/j.issn.1000-5641.2021.03.007
基金项目: 国家自然科学基金 (11871328); 上海市科委重点项目 (18511103105); 上海市自然科学基金 (19ZR1414000)
详细信息
    通讯作者:

    柳银萍, 女, 教授, 研究方向为计算机数学和计算机软件与理论. E-mail: ypliu@cs.ecnu.edu.cn

  • 中图分类号: O175.29

An n-order expansion method for determining the upper bound of the order of finite series solutions

  • 摘要: 构造非线性演化方程有限级数解的直接代数方法都是基于齐次平衡原则发展起来的, 如双曲正切方法、Jacobi椭圆函数法、Painlevé截断展开法、CRE方法等. 这些方法中所求解的阶数都是由齐次平衡原则确定的. 本文进一步拓展了齐次平衡原则, 考虑了更多的平衡可能性, 提出了一种n阶展开方法来确定有限级数解可能的更高阶数. 通过将该方法应用到双曲正切方法中, 对所考虑的非线性演化方程确实获得了一些新的更高的阶数和新的解.
  • 图  1  平衡点分类示意图

    Fig.  1  Schematic diagram for the classification of balance points

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出版历程
  • 收稿日期:  2020-03-12
  • 刊出日期:  2021-05-01

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