In this article, symmetry technique is utilized to obtain new exact solutions of the Cattaneo equation. The infinitesimal symmetries, linear combinations of these symmetries, and corresponding similarity variables are determined, which lead to many exact solutions of the considered equation. By applying similarity transformations, the mentioned partial differential equation is reduced to some ordinary differential equations of second order. Solutions of these ordinary differential equations have yielded many exact solutions of the Cattaneo equation.

中文翻译：

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使用李对称变换的二维Cattaneo模型的精确解

在本文中，利用对称技术获得Cattaneo方程的新精确解。确定了无限小对称性，这些对称性的线性组合以及相应的相似性变量，这导致了所考虑方程式的许多精确解。通过应用相似变换，将所提到的偏微分方程简化为一些二阶普通微分方程。这些常微分方程的解产生了Cattaneo方程的许多精确解。