对电信工程的随机高维非线性施罗丁格方程进行研究
Aziz Khan1, Jan Muhammad2, Usman Younas3
1Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
Scientific reports
|July 27, 2025
概括
本研究探讨了非线性随机施罗丁格方程的单一解,这对于理解复杂,杂环境中的波传播至关重要. 先进的分析方法揭示了多样化的光学单子行为,增强了非线性动力学的研究.
科学领域:
- 非线性动力学和数学物理
- 波浪现象是一种波浪现象.
- 随机过程 随机过程
背景情况:
- 非线性 (3+1) 维的随机施罗丁格方程模型波浪在噪音条件下的传播,对于光学和流体动力学等领域至关重要.
- 了解非线性和随机性之间的相互作用是解释阶段过渡和单元弹性等现象的关键.
研究的目的:
- 为了研究非线性 (3+1) 维的随机施罗丁格方程的多种单子解.
- 在各种物理参数下分析光学单子的行为.
- 证明先进的分析技术在解决复杂的非线性偏微分方程中的有效性.
主要方法:
- 应用先进的分析技术:修改的F扩展,Riccati扩展的修改的简单方程,和一般化的[公式:见文本]扩展方法.
- 使用波变换,将非线性部分微分方程转换为普通微分方程.
- 对不同参数值的单离子溶液进行图形分析.
主要成果:
- 识别众多单子溶液,包括明亮的,黑暗的,组合的,明暗的和单一的单子.
- 证明所采用的分析方法的效率和适应性.
- 在广泛的物理参数中对光学单子解决方案进行详细的研究.
结论:
- 该研究成功地确定了各种单子解决方案,突出了现代分析技术对非线性波现象的力量.
- 这些发现为现实,杂系统中非线性动态的行为提供了新的见解.
- 该研究有助于更深入地了解光学,流体动力学和等离子体物理学的复杂系统.
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