对于一个扩展 (3+1) 维的KP-Boussinesq方程的周期,n-soliton和可变分离解决方案
Chuanlin Shao1, Lu Yang2, Yongsheng Yan2
1School of Economics and Finance, Huaqiao University, Quanzhou, 362021, Fujian, People's Republic of China.
Scientific reports
|September 22, 2023
概括
研究人员探索了一个扩展的Kadomtsev-Petviashvili-Boussinesq方程,以找到周期和单一的解决方案. 开发了一种新的可变分离方法,产生了新的局部激发和对波相互作用的洞察.
科学领域:
- 数学物理 数学物理
- 非线性局部微分方程 不线性局部微分方程
- 索利顿理论是一个理论.
背景情况:
- 卡多姆茨夫-佩特维亚什维利-布西内斯克方程模型是各种物理系统中的波浪现象.
- 构建高维非线性方程的精确解决方案仍然是一个重大挑战.
- 了解局部激发及其动态对于许多物理领域至关重要.
研究的目的:
- 为了研究扩展 (3+1) 维的卡多姆茨夫-佩特维亚什维利-布西内斯克方程.
- 为了获得周期性溶液,n-soliton溶液和折叠的局部激发.
- 开发和应用一种新的可变分离方法来构建复杂的解决方案.
主要方法:
- 为了找到周期性解决方案,采用了Hirota的双线方法和Ansatz.
- 汉堡方程被用作获得n-soliton和n-冲击波解的辅助函数.
- 引入了一种新的可变分离方法,并应用于构建局部激发解决方案.
主要成果:
- 定期溶液和n-soliton溶液成功地得到了衍生.
- 构建了具有有趣相互作用动态的新折叠局部激发解决方案.
- 变量分离方法提供了溶液的直接分析形式.
结论:
- 该研究成功地构建了扩展 (3+1) 维的卡多姆茨夫-佩特维亚什维利-布西内斯克方程的各种类型的解决方案.
- 开发的变量分离方法为高维非线性局部微分方程提供了简单的方法.
- 这些发现有助于理解波浪现象和对非线性系统的分析处理.
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