Invariant analysis of the multidimensional Martinez Alonso–Shabat equation

Naseem Abbas, Akhtar Hussain, Muhammad Waseem Akram, Shah Muhammad, Mohammad Shuaib
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Abstract

This present study is concerned with the group-invariant solutions of the (3 + 1)-dimensional Martinez Alonso–Shabat equation by using the Lie symmetry method. The Lie transformation technique is used to deduce the infinitesimals, Lie symmetry operators, commutation relations, and symmetry reductions. The optimal system for the obtained Lie symmetry algebra is obtained by using the concept of the adjoint map. As for now, the considered model equation is converted into nonlinear ordinary differential equations (ODEs) in two cases in the symmetry reductions. The exact closed-form solutions are obtained by applying constraint conditions on the symmetry generators. Due to the presence of arbitrary functional parameters, these group-invariant solutions are displayed based on suitable numerical simulations. The conservation laws are obtained by using the multiplier method. The conclusion is accounted for toward the end.
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多维马丁内斯-阿隆索-沙巴特方程的不变分析
本研究利用李对称方法研究 (3 + 1) 维马丁内斯-阿隆索-沙巴方程的群不变解。本研究利用李氏变换技术推导出无穷小、李氏对称算子、换元关系和对称性还原。利用邻接图的概念,可以得到所获得的李对称代数的最优系统。目前,所考虑的模型方程在对称性还原的两种情况下被转换为非线性常微分方程(ODE)。通过对对称生成器施加约束条件,可以得到精确的闭式解。由于存在任意函数参数,这些组不变解是基于适当的数值模拟显示出来的。守恒定律是通过乘法器方法获得的。最后给出结论。
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