局部波和动态分析的相互作用在新的概括的随机分数潜力-KdV方程中
Yan Zhu1, Chuyu Huang1, Shengjie He2
1College of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, People's Republic of China.
Chaos (Woodbury, N.Y.)
|November 6, 2024
概括
研究人员开发了一种新的神经网络方法来解决概括的随机分数潜力-Korteweg-de Vries方程,为非线性光学和等离子体物理学找到复杂的分析解决方案.
科学领域:
- 应用数学和物理学的应用.
- 非线性动力学是一种非线性动力学.
- 计算科学 计算科学
背景情况:
- 概括的随机分数潜力-Korteweg-de Vries方程模型现象在非线性光学,光子传播,和多元件等离子体.
- 解决这些复杂的非线性局部微分方程的现有方法在生成多样化和罕见的分析解决方案时经常面临局限性.
研究的目的:
- 为了增强改进的双线神经网络方法来解决概括的随机分数潜力-Korteweg-de Vries方程.
- 以更高的效率产生复杂和罕见的分析解决方案,包括一次性流波和相互作用解决方案.
主要方法:
- 开发了一种增强的双线神经网络方法,利用许多激活功能而不是传统的神经元来模拟更少参数的复杂功能.
- 该方法包含了限制,以显著减少计算工作负载.
- 特定的神经网络架构 (例如"2-3-1") 使用Maple软件构建和实施,用于分析解决方案导出.
主要成果:
- 该研究成功地获得了许多精确的分析解决方案,包括双周期块解决方案,块 - 流波解决方案和三相互作用解决方案的叠加.
- 与通过常规方法获得的波形相比,衍生解决方案呈现出更复杂的波形.
- 这种新方法在分数顺序的非线性部分微分方程中显示出了显著的优势.
结论:
- 增强的神经网络方法为发现非线性分数顺序方程的复杂分析解决方案提供了强大的工具.
- 这些发现对理解非线性光学单子,电路中的光子传播和多元组件等离子体动力学具有重要意义.
- 这种方法预计将在研究非线性部分微分方程中得到更广泛的应用.
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