Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

• 作者: Cheng-Shi Liu
• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2021,（4）
• 所属期刊栏目: MATHEMATICAL PHYSICS
• 页码范围: 58-62
• 页数: 5页
• 语种: 英文

摘要

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.