数学论坛系列报告 2022年第1讲

报告题目：Traveling wave solutions of the perturbed generalized BBM equation and KdV equation:an Abelian integral analytical approach

报告人：陈爱永教授

报告时间：2022年4月19日14：00-15：00

报告地点：数学与统计学院一楼会议室

报告摘要：The existence of solitary waves and periodic waves for the perturbed generalized BBM equation is established by using geometric singular perturbation theory. It is proven that the wave speed c_0(h) is decreasing on $h\in[0,1/12]$ by analyzing the ratio of Abelian integrals. The upper and lower bounds of the limit wave speed are given. Moreover, the relation between the wave speed and the wavelength of traveling waves is obtained. For the perturbed generalized KdV equation, if n =2, 3, 4, we proved that limit wave speed $c_0(h)$ is also a decreasing function, but for arbitrary integer $ n>=5$, the monotonicity problem is still open.

报告人简介：陈爱永教授，湖南第一师范学院教授，硕士生导师。主要研究领域是微分方程与动力系统。主持完成了多项国家自然科学基金项目，获湖南省“芙蓉学者奖励计划”青年学者，广西杰出青年基金，广西自然科学二等奖，第十三届广西青年科技奖，入选湖南省121创新人才培养工程第二层次人选。在《Studies in Applied Mathematics》,《Journal of Differential Equations》,《Discrete and Continuous Dynamical Systems-A》、《中国科学》等期刊发表多篇学术论文。