报告题目: | Geometric singular perturbation analysis to a perturbed $(1 + 1)$-dimensional dispersive long wave equation |
报 告 人: | 夏永辉 教授 (浙江师范大学) |
主 持 人: | 王锦荣 教授 |
报告时间: | 2022年10月10日(星期一)下午 14:30-15:30 |
腾讯会议: | 腾讯会议ID:723-2246-4372 |
报告摘要:The existence of the solitary wave and the nonexistence of kink (anti-kink) wave solutions are studied for a perturbed $(1 + 1)$-dimensional dispersive long wave equation. The methods are based on the geometric singular perturbation {(GSP, for short)} approach, Melnikov method and bifurcation analysis. The results show that the solitary wave solution with a suitable wave speed $c$ and parameter ${\kappa}$ exists under the small singular perturbation. Interestingly, unlike solitary wave solutions, the kink (anti-kink) wave solution doesn't persist because the corresponding Melnikov function has no zeros. Further, numerical simulations are utilized to verify the correctness of our analytical results.
报告人简介: 夏永辉, 浙江师范大学特聘教授、博士生导师,获省部级科技奖励3项,入选“闽江学者特聘教授”。近年来主持国家自然科学基金3项(其中面上2项),参与国家重点项目1项,在本学科方向的SCI期刊《Proc. Amer. Math. Soc.》、《J. Differential Equations》、《SIAM J. Appl. Math.》、《Studies. Appl. Math.》、《Proc. Edinburgh Math. Soc.》、《Phys. Rew. E.》、《中国科学》等发表系列学术论文。系统建立了四元数体上微分方程的基本框架,改进了非自治Hartman-Grobman线性化的主要结果。