维埃斯特拉斯圆周期背景上的Breather波解决方案用于 (2 + 1) 维的概括变量系数KdV方程
Jiabin Li1, Yunqing Yang2, Wanyi Sun1
1School of Information Science, Zhejiang Ocean University, Zhoushan 316022, China.
Chaos (Woodbury, N.Y.)
|February 28, 2024
概括
这项研究介绍了 (2+1) 维的一般化变量系数Korteweg-de Vries (gvcKdV) 方程的Nth Darboux转换. 它在周期性背景上推导出广义的拉梅型和非线性波解,分析它们的动态.
科学领域:
- 非线性局部微分方程 不线性局部微分方程
- 数学物理 数学物理
- 索利顿理论是一个理论.
背景情况:
- (2+1) 维的一般化变量系数Korteweg-de Vries (gvcKdV) 方程是非线性科学的重要模型.
- 了解其解决方案,特别是复杂的背景,对于各种物理现象至关重要.
- 之前的研究已经探讨了具体的案例,但对周期性背景的概括解决方案需要进一步调查.
研究的目的:
- 为 gvcKdV 方程开发 Nth 达布克斯变换.
- 用拉梅函数方法推导泛化的拉梅型和非线性波解.
- 在静态和移动的Weierstrass圆函数周期背景上分析这些解决方案的动态和特性.
主要方法:
- 第一个达布克斯转换的应用.
- 使用拉梅函数方法来解决相关的线性光谱问题.
- 在韦尔施特拉斯圆形函数周期背景上导出解决方案.
主要成果:
- 为线性光谱问题得出了广义的拉梅式解决方案.
- 在静态和移动的Weierstrass圆函数周期背景上获得了非线性波解.
- 通过取半周期的极限来找到退化解决方案,并将解决方案动态与方程系数联系起来.
结论:
- 这项研究成功地为构建gvcKdV方程的复杂解决方案提供了一种方法.
- 衍生的解决方案表现出丰富的动态行为,受到背景潜力和方程系数的影响.
- 这项工作有助于理解变系系数系统中的非线性波现象.
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