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（湖南第一师范学院）

报告时间：2021年4月7日17:00-18:30

报告地点：数理楼145报告厅

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.

个人简历：陈爱永，博士，教授，硕士生导师, 湖南第一师范学院数学研究所所长，中国数学会奇异摄动专业委员会委员，湖南省“芙蓉学者奖励计划”青年学者，湖南省121创新人才工程第二层次人选，广西杰出青年科学基金获得者。研究方向：微分方程与动力系统。主持完成国家自然科学基金项目2项，曾获“广西自然科学奖二等奖”、“第十三届广西青年科技奖”。 已在 《J. Differential Equations》，《Discrete and Continuous Dynamical Systems-A》，《Studies in Applied Mathematics》和《中国科学》等国内外期刊发表论文近30篇。