报告题目：Higher order peakons and pseudo-peakons for generalized J-K-CH equations
报 告 人：姚若侠 教授
报告时间：2025年11月21日（星期五）下午14:30
报告地点：上海理工大学卓越楼，810会议室
报告摘要：Traditional methods for investigating peakon and pseudo-peakon waves face significant limitations when applied to higher order integrable systems, such as the generalized higher order Camassa-Holm (CH), Degasperis-Procesi (DP), and b-family Novikov equations. We study the generalized higher order CH equations (J-K-CH), encompassing four cases J-1-CH，J-2-CH, J-3-CH , and the general case J-K-CH. By analyzing weak solutions of the generalized J-K-CH type equations, leveraging the properties of the signum function, the generalized function/distribution function, and the zero distribution analysis, we construct a theoretical framework for generating and rigorously verifying conjectures on the existence of the higher order peakons and pseudo-peakons. Furthermore, we derive constraint conditions for unified mathematical expressions describing peakons and higher order pseudo-peakons, characterized by arbitrary constants: a 5th-order pseudo-peakon with J-4 arbitrary constants for J-1-CH equation, a 7th-order pseudo-peakon with J-6 arbitrary constants for J-2-CH equation, a 9th-order pseudo-peakon with J-8 arbitrary constants for J-3-CH equation, and a (2K+3)th-order pseudo-peakon with J-2(K+1) arbitrary constants for the generalized J-K-CH equation. Besides, more higher order pseudo-peakon are given for some specific parameter constraints by analyzing the continuity condition and the singularity condition.
报告人简介:姚若侠，陕西师范大学三级教授，博士生导师，现任人工智能与计算机学院院长，全国高等学校计算机教育研究会师范教育分会副理事长，曾任陕西师范大学学科建设处处长，人才工作处处长等职。西北大学数学系本科，华东师范大学计算机系硕士、博士，上海交通大学博士后，美国明尼苏达大学数学系访问学者；陕西师范大学符号计算与人工智能实验室主任；主持完成国家自然科学基金面上项目3项、省部级项目4项；研究成果在国内外重要期刊发表；2018年以第一完成人获陕西省科学技术奖二等奖1项，2006年以第三完成人获陕西省科学技术奖二等奖1项，博士论文获上海市研究生优秀成果奖(优博论文)。