In the paper, we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions. We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity. And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept. Our mathematical tool is the logarithmic trial equation method.

中文翻译：

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具有二阶对数非线性的两个模型方程式及其高斯解

在本文中，我们试图研究高对数非线性波动中高斯波存在的机理。我们首先构造两个模型方程，其中包括高阶色散和二次对数非线性。然后证明了如果保持色散和对数非线性之间的平衡，则高斯波可以存在于高对数非线性波动方程中。我们的数学工具是对数试用方程法。