【报告题目】Nonlinear wave transitions and their mechanisms of (2+1)-dimensional Sawada-Kotera equation
【报 告 人】田守富教授 中国矿业大学
【报告时间】10月25日下午2:00
【腾讯会议号】690 646 741
【报告摘要】In this talk, we discuss the transitions and mechanisms of nonlinear waves in the (2+1)-dimensional Sawada-Kotera (2DSK) equation are studied by means of characteristic line and phase shift analysis, and the dynamic behavior of various nonlinear transformed waves. Firstly, we obtain the N-soliton solution based on the Hirota bilinear method, from which the breath wave solution is constructed by changing the parameters into a complex form in pairs, and lump solution is obtained via the long wave limit method. Then the mechanism of the breath wave solution transformation is studied by characteristic line analysis, we present the types of transformed nonlinear waves, including quasi-anti-dark soliton,M-shaped soliton, W-shaped soliton, multi-peak soliton, and quasi-periodic wave soliton, and the distribution diagrams of these nonlinear waves on the (α, β) plane is rendered. We further reveal the gradient properties of the transformed wave. In addition, the transformed wave is decomposed into a solitary wave and a periodic wave component, and the formation mechanism, locality, and oscillation properties of the nonlinear transformed wave are explained through the nonlinear superposition. Furthermore, we demonstrate that the geometric properties of the characteristic lines vary with time essentially resulting in the time-varying properties of nonlinear waves, which have never been found in (1+1)-dimensional systems. Based on high-order nonlinear waves, the state transitions of the mixed solution and the second-order breath wave solution are investigated. We show several collision models of nonlinear waves, and reveal that the phase shift difference between the solitary and the periodic wave component leads to the deformable collision of the transformed wave. Such phase shift is due to time evolution and wave interaction. Finally, the dynamic process of nonlinear wave collision under the combined action of time and collision is presented.
【报告人简介】田守富，中国矿业大学特聘研究员、博士生导师；曾获全球前2%顶尖科学家榜单、爱思唯尔中国高被引学者、辽宁省自然科学二等奖、淮海科技二等奖、英国皇家物理学会高被引中国作者奖等；主要研究方向是孤立子理论、可积系统、Riemann-Hilbert问题；近年来，主持国家自然科学基金青年和面上项目、江苏省自然科学基金面上项目等多项研究课题；在Journal of Differential Equations ，Proceedings of the Royal Society A，Studies in Applied Mathematics，Physica D， Proceedings of the AMS，Journal of Physics A和中国科学上发表学术论文多篇 。
【邀请人】林机教授
欢迎各位老师和学生参加！
