报告题目：Abelian integral analysis in a quartic KdV equation with multiple dissipation

报告时间：2024年11月6日周三16：00—17：30

报告地点：腾讯会议124-248-551

报告摘要：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 Poincar´e 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.

报告人简介：孙宪波，杭州师范大学教授。研究方法为微分方程定性理论及其应用，在JDE、SCM、DCDS B，JSC，BSM等国际主流期刊上发表学术论文三十余篇。主持国家自然科学基金项目4项，省部级项目多项。