In this paper, first, we will try to introduce the gravitational domain wall as a physical system. In the second step, we also introduce the Hun differential equation as a mathematical tools. We factorize the known Heun’s equation as form of operators [Formula: see text], [Formula: see text] and [Formula: see text]. Then we compare the differential equation of gravitational domain wall with corresponding Hun equation. In that case the above-mentioned operators can be obtained for the gravitational system by the comparing process. Finally, we employ such operators and achieve the corresponding symmetry algebra with the usual commutation relation of operators to each other. Here, by having such operators, we investigate the stability of system.

中文翻译：

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引力畴壁与一些对称代数的稳定性

在本文中，首先，我们将尝试将引力畴壁作为一个物理系统来介绍。第二步，我们还引入了匈奴微分方程作为一种数学工具。我们将已知的 Heun 方程分解为运算符 [Formula: see text]、[Formula: see text] 和 [Formula: see text] 的形式。然后我们将引力畴壁的微分方程与对应的Hun方程进行比较。在这种情况下，可以通过比较过程获得引力系统的上述算子。最后，我们使用这样的算子，用算子之间通常的对易关系来实现相应的对称代数。在这里，通过拥有这样的算子，我们研究了系统的稳定性。