報(bào)告題目：Abelian integral analysis in a quartic KdV equation with multiple dissipation

報(bào)告時(shí)間：2024年11月6日周三16：00—17：30

報(bào)告地點(diǎn)：騰訊會(huì)議124-248-551

報(bào)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.

報(bào)告人簡(jiǎn)介：孫憲波，杭州師范大學(xué)教授。研究方法為微分方程定性理論及其應(yīng)用，在JDE、SCM、DCDS B，JSC，BSM等國(guó)際主流期刊上發(fā)表學(xué)術(shù)論文三十余篇。主持國(guó)家自然科學(xué)基金項(xiàng)目4項(xiàng)，省部級(jí)項(xiàng)目多項(xiàng)。