报告题目：一个形变布森尼斯克方程的贝克隆变换与无穷多新的显式精确解

报告人：尚亚东 教授

报告时间：2024年10月29日下午14:30-15:30  

报告地点：腾讯会议：386-146-178

报告摘要：In this talk, I will deal with a variant Boussinesq equations which describe the propagation of shallow water waves in a lake or near an ocean beach. We derive out two hetero-Backlund transformations between the variant Boussinesq equations and two linear parabolic equations by using the extended homogeneous balance method. We also obtain two hetero-Backlund transformations between the    variant Boussinesq equations and Burgers equations. Furthermore, we obtain two hetero-Backlund transformations between the variant Boussinesq equations and heat equations. By using these transformations and so-called “seed solutions”, we obtain a large number of explicit exact solutions of the variant Boussinesq equations. Especially, The infinite explicit exact singular solutions of the equation variant Boussinesq equations are obtained for the first time. It is worth noting that these singular wave solutions of the variant Boussinesq equations will blow up on some lines or curves in the (x,t) plane. These facts reflect the complexity of the structure of the solution of the variant Boussinesq equations. It also reflects the complexity of shallow water wave propagation from one aspect.

主讲人简介：尚亚东，广州大学数学学院教授，博士生导师. 现在楚雄师范学院数学与计算机学院任教。分别在兰州大学、西北工业大学取得学士、硕士及博士学位。 主要从事非线性偏微分方程理论与应用研究，目前感兴趣的方向有非线性发展方程定性理论，无穷维动力系统理论、孤立子与可积系统理论。 主持参与多项国家自然科学基金和广东省基金项目，在国内外发表学术论文120余篇，其中被Sci收录70余篇，国内重要期刊发表40余篇.