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格罗斯-皮塔耶夫斯基系统的复杂单独波模式:在量子和光学工程中的应用
Muhammad Bilal1, Yazen M Alawaideh2, Shafqat Ur Rehman3
1Department of Physics, Shanghai University, Shanghai, 200444, China.
Scientific reports
|December 22, 2025
概括
本研究使用先进的方法探索分数多元件格罗斯-皮塔耶夫斯基方程的精确单子解. 这些发现为物理学和材料科学中的非线性现象提供了洞察力.
科学领域:
- 非线性物理学 非线性物理学
- 量子力学就是量子力学.
- 凝聚物质物理学 凝聚物质物理学
背景情况:
- 多元组件的格罗斯-皮塔耶夫斯基方程模拟了诸如斯-爱因斯坦凝结体之类的现象.
- 了解其复杂的动态需要精确的分析解决方案,特别是单一的解决方案.
- 分数计算为分析这些非线性系统提供了一个新的框架.
研究的目的:
- 为了研究复杂的分数Gross-Pitaevskii方程的精确单子解.
- 将分数分析,特别是β导数,应用于这个基本的非线性施罗丁格方程.
- 发现新的光学解决方案并分析它们的特性.
主要方法:
- 使用β-导数进行分数分析.
- 应用了新的扩展型超标函数方法 (EHFM).
- 采用统一方法解决非线性部分微分方程.
- 使用Wolfram Mathematica通过反置换验证解决方案.
主要成果:
- 获取多样化的光学解决方案,包括三角形,形,理性函数和复杂的多重单元结构.
- 通过EHFM和统一方法发现新的解决方案.
- 波形状的可视化和对β导数的参数影响的分析.
结论:
- 该研究为分析各种物理环境中的复杂非线性现象提供了有效的框架.
- 获得的解决方案及其可视化增强了对潜在实际应用的理解.
- 格罗斯-皮塔耶夫斯基方程的微分分析揭示了对超流动性和超导性的重要见解.
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