论文标题
Jimbo-Miwa方程和概括的谎言对称分析和相似解决方案
Lie Symmetry Analysis and Similarity Solutions for the Jimbo-Miwa Equation and Generalisations
论文作者
论文摘要
正如Wazwaz等人提出的，使用Lie的群体方法，我们研究了Jimbo-Miwa方程及其两种扩展形式。有趣的是，所有三个方程式的旅行波解决方案都是相似的。此外，我们获得了某些新的减少，这些降低对于三个方程中的每个方程式中的每个方程式都是完全不同的。例如，对于Jimbo-Miwa方程的扩展形式之一，随后的还原导致带有超几何溶液的二阶方程。在某些降低中，我们获得了更简单的一阶和可线二阶方程，这有助于我们构建分析解决方案作为封闭形式的函数。对于每种不同形式的Jimbo-Miwa，非零的括号的变化也呈现出不同的视角。最后，应用奇异性分析以确定还原方程的整合性和Jimbo-Miwa方程的不同形式。
We study the Jimbo-Miwa equation and two of its extended forms, as proposed by Wazwaz et al, using Lie's group approach. Interestingly, the travelling-wave solutions for all the three equations are similar. Moreover, we obtain certain new reductions which are completely different for each of the three equations. For example, for one of the extended forms of the Jimbo-Miwa equation, the subsequent reductions leads to a second-order equation with Hypergeometric solutions. In certain reductions, we obtain simpler first-order and linearisable second-order equations, which helps us to construct the analytic solution as a closed-form function. The variation in the nonzero Lie brackets for each of the different forms of the Jimbo-Miwa also presents a different perspective. Finally, singularity analysis is applied in order to determine the integrability of the reduced equations and of the different forms of the Jimbo-Miwa equation.
