类似 (3+1) 维的Hirota双线式方程的高阶理性类型解
Wenting Li1, Ailing Jiao2, Wei Liu1
1Qiongtai Normal University, Haikou 571127, China.
Mathematical biosciences and engineering : MBE
|December 5, 2023
概括
研究人员构建了一个新的 (3+1) 维的希罗塔双线式方程 (HBLE),并使用广义的希罗塔双线式方法推导出六组通用解决方案. 分析了高阶理性解决方案的动态行为.
科学领域:
- 非线性局部微分方程 不线性局部微分方程
- 数学物理学的数学物理.
- 动态系统 动态系统
背景情况:
- 对非线性偏微分方程的研究对于各种科学领域的复杂现象建模至关重要.
- 希罗塔双线方程是一个重要的方程类,以其精确的解而闻名.
- 扩展现有的模型,如 (3+1) 维的Hirota双线方程,可以揭示新的数学结构和物理见解.
研究的目的:
- 构建和分析一个新的 (3+1) 维动态系统方程,称为Hirota双线式方程 (HBLE).
- 为新建的HBLE.LE推导和研究高阶的理性解决方案.
- 探索这些解决方案的分析性条件和动态行为.
主要方法:
- 应用广义的Hirota双线方法来导出 (3+1) 维的HBLE.
- 从一个关联的通用双线方程的多项式解中生成高阶的理性解.
- 使用像Maple这样的计算工具分析解决方案的分析性和动态性质.
主要成果:
- 成功构建了 (3+1) 维的希罗塔双线式方程 (HBLE),并添加了一些非线性项.
- 一组高阶理性解决方案的推导.
- 确定六个不同的一般解决方案组,满足分析性条件.
- 获得的理性解决方案的动态行为的可视化和分析.
结论:
- 广义的Hirota双线方法对于构建新的可集成方程并找到它们的解决方案是有效的.
- 新衍生的HBLE提供了一个研究复杂非线性现象的平台.
- 高阶理性解决方案表现出有趣的动态行为,需要进一步调查.
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