Abelian integral analysis in a quartic KdV equation with multiple dissipation

主 讲 人 ：孙宪波    教授

活动时间：11月15日18时30分    

地      点 ：数学科学学院D2022

讲座内容：

We investigate solitary and periodic waves for a quartic Kortewegde Vries (KdV) equation that incorporates multiple dissipative effects. Our primary focus is on the dynamical behaviors exhibited in a two-dimensional invariant flow. We establish the existence of solitary waves by evaluating the associated Abelian integral along a homoclinic loop, a technique that provides insights into their stability and existence. Additionally, we derive periodic traveling waves through a rigorous analysis of degenerate Hopf bifurcation, homoclinic bifurcation, and Poincare bifurcation. These bifurcations are crucial for elucidating the conditions under which a unique periodic traveling wave emerges, as well as scenarios in which two such waves coexist, including the intriguing coexistence of a solitary wave and a periodic wave. Our findings contribute valuable insights into the complex dynamics of the KdV equation when multiple dissipative factors are considered.

主讲人介绍：

孙宪波，杭州师范大学数学学院教授，博士生导师。研究方向为微分方程定性理论，在中国科学，DCDS B，JDE，JSC，BSM等知名期刊发表学术论文三十余篇，主持三项国家自然科学基金，多项含广西杰出青年基金在内的省部级项目。

发布时间：2024-11-15 08:56:03