报告题目:高维非线性波的时变动力学

报告人：王雷教授 (北京华北电力大学）

报告时间：2022年5月26日 14:00-15:00

报告地点：腾讯会议 412896826

摘要：

In this talk, we discuss the dynamics of transformed nonlinear waves in the (2+1)-dimensional Ito equation by virtue of the analysis of characteristic line and phase shift. First, the N-soliton solution is obtained via the Hirota bilinear method, from which the breath-wave solution is derived by changing values of wave numbers into complex forms. Then, the transition condition for the breath waves is obtained analytically. We show that the breath waves can be transformed into various nonlinear wave structures including the multi-peak soliton, M-shaped soliton, quasi-anti-dark soliton, three types of quasi-periodic waves, and W-shaped soliton. The correspondence of the phase diagram for such nonlinear waves on the wave number plane is presented. The gradient property of the transformed solution is discussed through the wave number ratio. We study the mechanism of wave formation by analyzing the nonlinear superposition between a solitary wave component and a periodic wave component with different phases. The locality and oscillation of transformed waves can also be explained by the superposition mechanism. Furthermore, the time-varying characteristics of high-dimensional transformed waves are investigated by analyzing the geometric properties (angle and distance) of two characteristic lines of waves, which do not exist in (1+1)-dimensional systems. Based on the high-order breath-wave solutions, the interactions between those transformed nonlinear waves are investigated, such as the completely elastic mode, semi-elastic mode, inelastic mode, and collision-free mode. We reveal that the diversity of transformed waves, time-varying property, and shape-changed collision mainly appear as a result of the difference of phase shifts of the solitary wave and periodic wave components. Such phase shifts come from the time evolution as well as the collisions. Finally, the dynamics of the double shape-changed collisions are presented.

报告人简介：

王雷，毕业于北航流体力学研究所，英国爱丁堡大学数学系访问学者，华北电力大学教授、博士生导师。近年来主要研究方向为非线性波的计算与机制分析，人工智能在非线性动力学中的应用，人工智能在热防护和能源环保数字孪生系统中的应用等。主持国家自然科学基金四项，博士后基金面上和特助两项，中央高校基金三项，相关结果发表在Physica D, Proceedings of the Royal Society A, Physical Review E, Chaos, Annals of Physics, Physics of Plasmas, EPL, PLA等重要学术刊物。担任国家自然科学基金评议人，教育部学位中心专业学位水平评估专家以及Nonlinearity, Proceedings of the Royal Society A, Journal of Optics, Ocean Engineering等多个学术期刊的评审人。

邀请人：马立媛