【报告题目】Formation of the undular bores in shallow water generalized Kaup-Boussinesq model
【报告人】王灯山教授，北京师范大学教授
【报告时间】2022年11月8日下午3：00，
【腾讯会议号】731 930 595
【报告摘要】The formation of undular bores in Riemann problems of the good generalized Kaup-Boussinesq equation is investigated by Whitham modulation theory. Firstly, the Whitham equations associated with the one-phase and two-phase periodic wave solutions are given by the finite-gap averaging method. Secondly, the basic structures of rarefaction wave and dispersive shock wave are discussed by considering the self-similar solutions of the Whitham equations. Then we propose a complete classification of all possible wave patterns for the initial discontinuity of the good generalized Kaup-Boussinesq equation, in which it has been shown that the theoretical results from Whitham modulation theory are in good agreement with the full numerical simulations. The correspondences between the soliton frontiers of the dispersive shock waves and the exact soliton solution of the good generalized Kaup-Boussinesq equation are considered, and exotic undular bores are found. Finally, the dam break problem and piston problem are explored to show the important physical applications of the theoretical results, from which certain inspiring phenomena of wave breaking are discovered for the first time.
【报告人简介】王灯山，北京师范大学数学科学学院，教授、博士生导师。主要从事可积系统和渐近分析方面的研究，在Analysis & PDE, Physical Review Letters, J. Differential Equations, J. Nonlinear Science 和Physica D等国际期刊发表学术论文90余篇，主持国家自然科学基金面上项目等国家级和省部级项目10余项，曾获得茅以升北京青年科技奖，并参与获得北京市科学技术奖一等奖。
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