【报告题目】A review on Darboux transformations some coupled KdV systems
【报 告 人】刘青平教授 中国矿业大学
【腾讯会议号】951 506 087
【报告摘要】In the soliton theory, the KdV equation is the most important system. This celebrated system has been generalized in various ways. In this talk, we consider the coupled KdV systems and their Darboux transformations. We will demonstrate how the relevant Darboux transformations may be constructed.
【报告题目】Whitham modulation theory and its applications to the initial discontinuity of integrable systems
【报 告 人】王灯山教授，北京师范大学
【腾讯会议】951 506 087
【报告摘要】The classification of solutions to the integrable nonlinear wave equations with discontinuous initial data is considered by Whitham modulation theory. We first report our work on the complete classification of solutions to the defocusing complex modified Korteweg-de Vries equation with the step-like initial condition. Then introduce our recent exploration on the Jaulent-Miodek equation and defocusing AB system with step-like initial data. It is noted that the direct numerical simulations of these integrable systems are agreed well with the solutions corresponding to Whitham modulation theory, which verifies the validity of results from Whitham modulation theory.