In this paper, it is considered a quasi-linear strongly-damped wave equation defined by a non-linear partial differential equation of third order. The equation describes motions of viscoelastic solids. We study the conservation laws of this equation. By applying the multiplier method of Anco and Bluman to the equation, we find the multipliers. Consequently, we obtain a complete classification of conservation laws. Moreover, we use the Lie-group theory to analyse the symmetries of the equation. From the Lie symmetries, all the reductions are determined. Afterwards, we construct exact solutions with physical interest: travelling wave solutions.

中文翻译：

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拟线性强阻尼波动方程的守恒定律与对称性分析

在本文中，它被认为是由三阶非线性偏微分方程定义的拟线性强阻尼波动方程。该方程描述了粘弹性固体的运动。我们研究这个方程的守恒定律。通过将 Anco 和 Bluman 的乘法器方法应用于方程，我们找到了乘法器。因此，我们得到了一个完整的守恒定律分类。此外，我们使用李群理论来分析方程的对称性。根据李对称性，可以确定所有的约简。之后，我们构建具有物理意义的精确解：行波解。