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在共振非线性施罗丁格系统中,通过增强的修改扩展的tanh函数方法,具有立方五子效应的soliton动态和稳定性
Amany Tarek1, Hamdy M Ahmed2, Niveen Badra3
1Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, Egypt. amany.tarek@eng.asu.edu.eg.
Scientific reports
|December 1, 2025
概括
研究人员探索了一个复杂的非线性施罗丁格方程的单一波解决方案. 该研究成功地确定了各种精确的解决方案,包括明亮和黑暗的单子,证明了对波动力学的参数控制.
科学领域:
- 非线性动力学是一种非线性动力学.
- 数学物理学的数学物理.
- 波浪的传播方式
背景情况:
- 非线性施罗丁格方程 (NLSE) 对于描述波浪现象至关重要.
- 研究具有复杂非线性性的高维NLSE对于理解高级波浪行为至关重要.
- 孤独波解决方案是描述非线性系统中稳定的波包的关键.
研究的目的:
- 寻找新的单一波解决方案,用于3D,时间依赖的NLSE,具有立方-五度效应和广义的库德里亚索夫型自相调制.
- 为复杂的非线性模型证明改进的修改扩展的tanh函数方法的有效性.
- 分析系统参数对单波动态和稳定性的影响.
主要方法:
- 应用了改进的修改扩展的tanh函数方法.
- 导出广泛的精确分析解决方案.
- 平衡点的线性稳定性分析和相位图分析.
主要成果:
- 获得了各种各样的孤独波解:明亮的孤独子,黑暗的孤独子,单数周期解,单数解,雅科比圆函数解,以及韦尔斯特拉斯圆双周期函数解.
- 证明系统参数显著控制单一波的振幅,宽度和动态.
- 展示了参数变化如何影响平衡状态的存在和消失.
结论:
- 改进的修改扩展的tanh函数方法对于生成高维非线性模型的精确解决方案非常有效.
- 这项研究扩大了已知的单波溶液目录,揭示了显著的结构多样性.
- 提供了关于非线性,稳定性和波浪演变的新理论见解,对非线性光学和等离子体物理学有影响.
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