Dynamical and statistical properties of soliton gas in the focusing Gardner equation
数学专题报告
报告题目(Title)：Dynamical and statistical properties of soliton gas in the focusing Gardner equation
报告人(Speaker)：许韬（中国石油大学（北京）教授）
地点(Place)：后主楼1223 （腾讯会议：685-654-5612 备用腾讯会议：453 850 0147）
时间(Time)：5月20日(周一)，上午10:00-11:00
邀请人(Inviter)：臧立名、王灯山
报告摘要
For the focusing Gardner equation, we first study the dynamical properties of pairwise soliton interactions based on the two-soliton solution and its degenerate cases. Next, with the inclusion of all types of two-soliton interaction scenarios, we quantitatively show that the bipolar soliton interactions have a greater contribution to the skewness and kurtosis than those with the unipolar case. Meanwhile, we obtain the spectral-parameter and soliton-amplitude ratios, at which the bipolar soliton interactions have the strongest effects on the skewness and kurtosis. Furthermore, we feature the dynamics of soliton gas (SG) with the inclusion of the strongest pairwise soliton interactions admitting the maximum attainable amplification AI=2. As the number of such soliton pairs increases, the third moment decreases in absolute while the fourth moment increases, the maximum values in the global wave field increase significantly while the minimum values exhibit a relatively modest increase. Also, a pronounced elevation in the tails of the global probability density functions is observed for positive wave amplitudes, indicating an increase in the number of extreme events within the wave field. Our findings may contribute to the realization of some controllable SG experiments in water waves.
主讲人简介
许韬，现为中国石油大学（北京）理学院教授，博士生导师。先后于北京航空航天大学和北京邮电大学获得学士和博士学位，曾受留学基金委资助访问过美国布法罗大学和加拿大麦克马斯特大学。主要从事可积系统和非线性数学物理方程研究，主持国家自然科学基金1项、北京市自然科学基金1项。近年来，在Studies in Applied Mathematics, Physica D、Proceedings A、Physical Review E、Journal of Physics A、Journal of Mathematical Physics等期刊发表第一、通讯作者论文40余篇，累计SCI他引次数达2000余次。
