双分线分析,调制不稳定性和单子解决方案的动态分析,用于用m-分数运算符的一般化 (3 + 1) 维非线性波形方程
Mohamed S Algolam1, Md Mamunur Roshid2, Mohammed Alsharafi3
1Department of Mathematics, College of Science, University of Ha'il, Ha'il, 55473, Saudi Arabia.
Scientific reports
|April 15, 2025
概括
本研究探讨了使用修改的简单方程方法对分数非线性波方程的单一解. 研究确定了各种波浪模式,并证实了该方法.
科学领域:
- 非线性动力学是一种非线性动力学.
- 数学物理 数学物理
- 分数微积分的计算.
背景情况:
- 非线性波形方程在描述各种科学学科中复杂现象方面是至关重要的.
- 分数计算提供了一种更细致的方法来建模具有记忆和遗传性质的系统.
- 对于先进的建模,研究带有分数导数的一般化 (3+1) 维P型非线性波形方程至关重要.
研究的目的:
- 分析一个一般化的 (3+1) 维的P型非线性波形方程与一个M分数导数 (M-fGP-NWE) 的二叉理论.
- 导出和描述M-fGP-NWE的各种单离子溶液.
- 探索复杂的波浪现象和拟议模型的调制不稳定性.
主要方法:
- 使用波变量将M-fGP-NWE转换为普通微分方程.
- 应用利略变换来获得一个动态系统.
- 分析相位图和哈密尔顿函数,以确定同临床和异临床轨道.
- 使用修改的简单方程 (MSE) 方法来导出单离子溶液.
主要成果:
- 通过阶段肖像分析识别单一,钟形和周期波溶液.
- 使用MSE方法,以超标,三角形和指数形式导出单离子溶液.
- 复杂的波浪现象的可视化使用3D,2D和密度图.
- 对M-fGP-NWE的调制不稳定性的分析.
结论:
- 证实MSE方法是解决复杂的分数非线性波形方程的高效可靠技术.
- 这项研究为M-fGP-NWE.WE提供了对单子溶液和波动力学的全面了解.
- 这些发现有助于推进非线性动力学和分数运算的应用.
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