通过使用改进的伯努利子方程函数方法,研究β导数的时空分数非线性演化方程的波动力学
Anamika Podder1, Mohammad Asif Arefin1, M Ali Akbar2
1Department of Mathematics, Jashore University of Science and Technology, Jashore, 7408, Bangladesh.
Scientific reports
|November 22, 2023
概括
研究人员开发了一种新方法,以找到复杂的非线性方程的移动波解决方案,从而提高我们对海洋波到光学物理学的现象的理解.
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.
- 波浪现象是一种波浪现象.
背景情况:
- 分数非线性克莱恩 - 戈登和修改的规则化的长波方程模拟了各种物理系统.
- 这些系统包括相对论电子,海洋动力学 (海,潮波),浅水波和非线性光学.
- 找到准确的解决方案对于理解和预测这些复杂的行为至关重要.
研究的目的:
- 为分数非线性克莱恩 - 戈登和修改的规则化的长波方程推导出新的和通用的闭形移动波解决方案.
- 应用改进的伯努利子方程函数方法,以β导数的意义.
- 验证获得的解决方案并证明方法的有效性.
主要方法:
- 采用了改进的伯努利次方程函数方法.
- 利用分数复杂波形转换将分数部分微分方程转换为普通微分方程.
- 使用计算软件 (Maple) 验证解决方案,并与现有文献进行比较.
主要成果:
- 产生了新的封闭形式的移动波解决方案,包括曲,单数单元,钟形和反钟形单元.
- 可视化解决方案波形,使用2D,3D和特定参数值的轮图.
- 证实了衍生解决方案的准确性和独特性.
结论:
- 改进的伯努利次方程函数方法对于寻找通用波解是有效的.
- 该方法为分析复杂的分数非线性模型提供了可靠和计算效率高的方法.
- 获得的解决方案为研究物理现象的动态提供了有价值的见解.
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