Dynamical and statistical properties of soliton gas in the focusing Gardner equation

许韬  教授

（中国石油大学（北京））

报告时间：2024年4月11日 (星期四) 上午9：30

报告地点: 沙河校区国实E502

报告摘要：Based on the exact two-soliton solution and its degenerate cases, we first study the dynamical properties of pairwise soliton interactions in the focusing Gardner equation (GE) by the asymptotic analysis method and extreme-value analysis technique. 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. Specifically, the spectral-parameter and soliton-amplitude ratios are specified when the bipolar soliton interactions have the strongest effects on the skewness and kurtosis. Furthermore, numerical simulations are conducted to examine the properties of soliton gas (SG), especially confirming the emergence of the soliton interactions described by the mixed and rational solutions in a denser soliton ensemble. In addition, we feature the dynamics of SG with the inclusion of the strongest pairwise soliton interactions admitting the maximum attainable amplification AI=2. Our findings may contribute to the realization of some controllable SG experiments in water waves.

报告人简介：许韬，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，现为中国石油大学（北京）理学院数学系教授，博士生导师，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2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。

邀请人： 王振

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