International Institute for Symmetry Analysis and Mathematical Modelling & Focus Area for Pure and Applied Analytics, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China.
J Adv Res. 2020 Oct 26;29:159-166. doi: 10.1016/j.jare.2020.10.002. eCollection 2021 Mar.
The purpose of this paper is to study, a (1 + 1)-dimensional generalised coupled modified Korteweg-de Vries-type system from Lie group analysis point of view. This system is studied in the literature for the first time. The authors found this system to be interesting since it is non-decouplable and possesses higher generalised symmetries.
We look for the closed-form solutions and conservation laws of the system.
Optimal system of one-dimensional subalgebras for the system was obtained and then used to perform symmetry reductions and construct group invariant solutions. Power series solutions for the system were also obtained. The system has no variational principle and as such, we employed the multiplier method and used a homotopy integral formula to derive the conserved quantities.
Group invariant solutions and power series solutions were constructed and three conserved vectors for the system were derived.
The paper studies the (1 + 1)-dimensional generalised coupled modified Korteweg-de Vries-type system for the first time and constructs its exact solutions and conservation laws.
本文旨在从李群分析的角度研究一个（1+1）-维广义耦合修正 Korteweg-de Vries 型系统。该系统在文献中首次被研究。作者发现该系统很有趣，因为它不可解耦并且具有更高的广义对称。
我们寻找该系统的封闭形式解和守恒律。
我们获得了该系统的一维子代数最优系统，然后使用它进行对称约化并构建群不变解。我们还得到了该系统的幂级数解。由于该系统没有变分原理，因此我们使用乘数法和同伦积分公式来推导守恒量。
构建了群不变解和幂级数解，并推导出该系统的三个守恒向量。
本文首次研究了（1+1）-维广义耦合修正 Korteweg-de Vries 型系统，并构建了其精确解和守恒律。
