Under investigation in this paper is a two-component Novikov system (also called Geng-Xue equation), which was proposed by Geng and Xue in 2009. Firstly, via the Lie symmetry method, infinitesimal generators, commutator table of Lie algebra and symmetry groups of the two-component Novikov system are presented. At the same time, some group invariant solutions are computed through similarity reductions. In particular, we construct peakon solution by applying the distribution theory. In addition, based on obtained group invariant solutions and symmetry transformations, we derive some new exact solutions, which include stationary solutions, smooth solutions, and a weak solution. The analytical properties to some of group invariant solutions and new exact solutions are discussed, such as decay, asymptotic behavior, and boundedness.

中文翻译：

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双分量 Novikov 系统解的解析研究

本文研究的是由耿和薛在2009年提出的二分量诺维科夫系统（也称为耿雪方程）。首先，通过李对称方法、无穷小生成元、李代数交换子表和对称群介绍了两分量 Novikov 系统。同时，通过相似性约简计算一些组不变解。特别是，我们通过应用分布理论构造了peakon解决方案。此外，基于得到的群不变解和对称变换，我们推导出了一些新的精确解，包括平稳解、光滑解和弱解。讨论了一些群不变解和新的精确解的解析性质，如衰变、渐近行为和有界性。