报告题目：Evolution of dispersive shock waves to the complex modified Korteweg–deVries equation with higher-order effects

报告人：李欣越教授，山东科技大学

报告时间：2025年5月14日（周三）10:00

报告地点：20-308

报告摘要：In this paper, new dispersive shock waves (DSWs) in step-like initial value problems to the complex modified Korteweg–de Vries equation with higher-order effects are found via Whitham modulation theory. For the aforementioned equation, the 1-genus and 2-genus periodic solutions and the associated Whitham equations which are used to describe DSWs are firstly given by the finite-gap integration method, and we also analyze nine types of rarefaction waves appearing before DSWs under the 0-genus Whitham equations. Subsequently, the DSW solutions with step-like initial data are discussed, where we acquire some DSW structures that have not been previously proposed. These notable new results include 1-genus DSW satisfying that one Riemann invariant is constant and the other three are variables and 2-genus DSW in the DSW solutions with one step-like initial data, as well as 3-genus DSW resulting from the collision to 1-genus and 2-genus or two 2-genus DSWs propagating toward each other in the possible DSW solutions with two step-like initial data. Ultimately, the dam break problem is explored to demonstrate the significant physical application of the theoretical findings.

报告人简介：李欣越教授，山东科技大学，博士，硕士生导师。研究领域：数学物理、孤子理论、可积系统及应用、哈密顿结构等。承担多项国家基金项目，共发表SCI文章60余篇。

邀请人：张翼