论文标题
谎言对称性和广义浅水方程的奇异性分析
Lie symmetries and singularity analysis for generalized shallow-water equations
论文作者
论文摘要
我们通过使用不变点转换理论和广义的Camassa-Holm方程和广义的本杰明 - 荷兰 - 马奥尼方程的奇异性分析进行完整的研究。从谎言理论中，我们发现两个方程在相同的三维谎言代数下是不变的，这是Camassa-Holm方程所接受的同一代数。我们确定了公认的谎言对称性的一维最佳系统，并对研究的两个方程式进行了完整的分类。通过使用点对称性或奇异性分析来研究还原方程。最后，奇点分析直接应用于偏微分方程，从我们推断我们研究的广义方程式通过奇异性测试并可以整合。
We perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm equation and the generalized Benjamin-Bono-Mahoney equation. From the Lie theory we find that the two equations are invariant under the same three-dimensional Lie algebra which is the same Lie algebra admitted by the Camassa-Holm equation. We determine the one-dimensional optimal system for the admitted Lie symmetries and we perform a complete classification of the similarity solutions for the two equations of our study. The reduced equations are studied by using the point symmetries or the singularity analysis. Finally, the singularity analysis is directly applied on the partial differential equations from where we infer that the generalized equations of our study pass the singularity test and are integrable.
