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报告题目：Integrable turbulence and statistical characteristics of chaotic wave field in the Kundu-Eckhaus equation

报告人：李敏 副教授（华北电力大学）

报告时间：2025年7月11日周五19：00-20：00

报告地点：腾讯会议426 871 662

报告摘要：Integrable turbulence, as an irregular behavior in dynamic systems, has attracted a lot of attention in integrable and Hamiltonian systems. This article focuses on the studies of integrable turbulence phenomena of the Kundu-Eckhaus (KE) equation as well as the generation of rogue waves from the numerical and statistical viewpoints. First, via the Fourier collocation method, we obtain the spectral portraits of different analytical solutions. Second, we perform the numerical simulation on the KE equation under the initial condition of a plane wave with random noise to simulate the chaotic wave fields. Then, we analyze the influences of standard deviation and correlation length on the integrable turbulence and amplitude of wave field. It’s found that both of the two parameters have positive effects on the generation probability of rogue wave caused by the interactions. But only the variation of standard deviation can lead to the transition from the breather turbulence to soliton turbulence. Furthermore, by analyzing the effects of additional higher-order nonlinear terms on the chaotic wave field, we find that those two higher-order nonlinear effects in the KE equation can lead to a larger amplitude of the chaotic wave field and a higher probability of generating rouge waves compared with the NLS equation.

报告人简介：李敏，华北电力大学副教授，硕士生导师，从事可积系统、数学物理方程的理论及应用研究，目前以第一、通讯作者发表SCI检索论文30余篇，其中Stud. Appl. Math.（1篇），Proc. R. Soc. A（1篇），Physica D（3篇），Phys. Rev. E（4篇）。所发表论文累计他引1400余次（Web of Science），相关研究成果以第一完成人获得了2024年河北省自然科学奖三等奖。在研主持国家自然科学基金面上项目1项、北京市自然科学基金面上项目1项和河北省自然科学基金面上项目1项，主持完成国家自然科学基金青年科学基金项目1项和数学天元基金项目1项。

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