【讲座题目】Darboux transformation, Adler-Moser Polynomials and vortex rings for the GP equation
【主 讲 人】黄晔辉
【讲座时间】2022.10.21周五上午10点半-11点半
【腾讯会议】ID：797-500-910
【报告人简介】黄晔辉，华北电力大学数理学院副教授。主要从事可积系统方面的研究，包括可积系统的形变，达布变换，反散射变换，Riemann-Hilbert方法等。
【讲座内容简介】Darboux transformation is a powerful tool in finding the relation of the solutions of integrable system.We construct polynomials as the solution of a special equation, which canbe regarded as a generalization of the classical Adler-Moser polynomials. Then we construct new finite energy traveling wave solutions with small speed for theGross-Pitaevskii equation. These solutions have the shape of 2n+1 vortex rings, far away from each other. Among these vortex rings, n+1 of them have positive orientation and the other n of them have negative orientation. The location of these rings are described by the roots of a sequence of polynomials with rational coefficients. This is joint work with Weiwei Ao, Yong Liu and Juncheng Wei.
