在经典的Boussinesq框架中,分数非线性波的单体结构和动态特征
Nasrin Nahar Rimu1, Md Antajul Islam1, Pinakee Dey2
1Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail, 1902, Bangladesh.
Scientific reports
|February 6, 2026
概括
这项研究探讨了分数Boussinesq方程,找到稳定的非线性波. 这些发现提升了对微分波现象的理解,例如浅水水力学等领域.
科学领域:
- 非线性动力学是一种非线性动力学.
- 流体力学 流体力学 流体力学
- 数学物理 数学物理
背景情况:
- 经典的Boussinesq方程模拟了浅水中的长波传播.
- 分数计算将微分方程扩展到非整数顺序,提供新的建模功能.
研究的目的:
- 调查时间空间分数的经典布西内斯方程.
- 分析非线性波的生成和动态.
主要方法:
- 修改扩展的tanh函数形式主义用于波解.
- 双叉理论和相平面分析用于动力学.
- 对强度进行灵敏度和线性稳定性分析.
主要成果:
- 确定了明亮/黑暗的单体,呼吸型波和周期波.
- 揭示了稳定和不稳定的波形状,有可能发生混乱的相互作用.
- 解决小扰动的解决方案的稳定性得到证实.
结论:
- 分数Boussinesq方程支持各种稳定的非线性波形.
- 这些发现促进了对非线性微分波现象的研究.
- 应用包括浅水水力学,等离子体物理学和格子系统.
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