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Lie symmetry analysis and similarity solutions for the Jimbo – Miwa equation and generalisations
Journal of Nonlinear, Complex and Data Science ( IF 1.5 ) Pub Date : 2020-11-18 , DOI: 10.1515/ijnsns-2019-0164 Amlan K. Halder 1 , Andronikos Paliathanasis 2, 3 , Rajeswari Seshadri 1 , Peter G. L. Leach 2, 4
Journal of Nonlinear, Complex and Data Science ( IF 1.5 ) Pub Date : 2020-11-18 , DOI: 10.1515/ijnsns-2019-0164 Amlan K. Halder 1 , Andronikos Paliathanasis 2, 3 , Rajeswari Seshadri 1 , Peter G. L. Leach 2, 4
Affiliation
Abstract 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.
中文翻译:
Jimbo-Miwa 方程的 Lie 对称分析和相似解及其推广
摘要 我们使用 Lie 群方法研究了 Wazwaz 等人提出的 Jimbo-Miwa 方程及其两种扩展形式。有趣的是,所有三个方程的行波解都是相似的。此外,对于三个方程中的每一个,我们都获得了某些完全不同的新约简。例如,对于 Jimbo – Miwa 方程的一种扩展形式,随后的缩减导致了具有超几何解的二阶方程。在某些归约中,我们获得了更简单的一阶方程和可线性化的二阶方程,这有助于我们将解析解构造为闭式函数。Jimbo – Miwa 的每种不同形式的非零李括号的变化也呈现出不同的视角。最后,
更新日期:2020-11-18
中文翻译:
Jimbo-Miwa 方程的 Lie 对称分析和相似解及其推广
摘要 我们使用 Lie 群方法研究了 Wazwaz 等人提出的 Jimbo-Miwa 方程及其两种扩展形式。有趣的是,所有三个方程的行波解都是相似的。此外,对于三个方程中的每一个,我们都获得了某些完全不同的新约简。例如,对于 Jimbo – Miwa 方程的一种扩展形式,随后的缩减导致了具有超几何解的二阶方程。在某些归约中,我们获得了更简单的一阶方程和可线性化的二阶方程,这有助于我们将解析解构造为闭式函数。Jimbo – Miwa 的每种不同形式的非零李括号的变化也呈现出不同的视角。最后,