The existence of solitary wave solutions of delayed Camassa-Holm equation via a geometric approach

发布时间：2018-11-26 作者：浏览次数：

Speaker:	杜增吉教授	DateTime:	2018年11月29日（周四）上午10:00-11:00
Brief Introduction to Speaker: 杜增吉，江苏师范大学教授。		Place:	六号楼四楼会议室
Abstract: In this talk, we discuss the Camassa-Holm equation, which is a model for shallow water waves. We first establish the existence of solitary wave solutions for the equation without delay. And then we prove the existence of solitary wave solutions for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using the method of dynamical system, especially the geometric singular perturbation theory and invariant manifold theory. According to the relationship between solitary wave and homoclinic orbit, the Camassa-Holm equation is transformed into the ordinary differential equations with fast variables by using the variable substitution. It is proved that the equation with disturbance also possesses homoclinic orbit, and there exists solitary wave solution of the delayed Camassa-Holm equation.