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。