论文标题
光束方程的相似解决方案和保护法：一项完整的研究
Similarity solutions and conservation laws for the Beam Equations: a complete study
论文作者
论文摘要
我们研究了相似性解决方案，并确定了各种形式的光束方程的保护定律，例如Euler-Bernoulli，Rayleigh和Timoshenko-Prescott。流浪波还会导致所有形式的可解决的四阶频率。另外，基于Euler-Bernoulli形式的缩放对称性的降低会导致某些ODES存在零对称性。因此，我们进行奇异性分析以确定整合性。我们研究了第二和第三次的两种降序频率。还原的二阶Ode是一种扰动的形式的Painlevé-Ince方程式，它是可集成的，三阶颂歌落入了Chazy，Bureau和Cosgrove研究的方程类别。此外，我们得出了上述梁形式的强制形式的对称性及其相应的减少和保护定律。对于所有情况，明确提到了谎言代数。
We study the similarity solutions and we determine the conservation laws of the various forms of beam equation, such as, Euler-Bernoulli, Rayleigh and Timoshenko-Prescott. The travelling-wave reduction leads to solvable fourth-order odes for all the forms. In addition, the reduction based on the scaling symmetry for the Euler-Bernoulli form leads to certain odes for which there exists zero symmetries. Therefore, we conduct the singularity analysis to ascertain the integrability. We study two reduced odes of order second and third. The reduced second-order ode is a perturbed form of Painlevé-Ince equation, which is integrable and the third-order ode falls into the category of equations studied by Chazy, Bureau and Cosgrove. Moreover, we derived the symmetries and its corresponding reductions and conservation laws for the forced form of the above mentioned beam forms. The Lie Algebra is mentioned explicitly for all the cases.
