The application of bidifferential calculus in integrable systems
数学专题报告
报告题目(Title)：The application of bidifferential calculus in integrable systems
报告人(Speaker)：张翼 教授（浙江师范大学）
地点(Place)：腾讯会议ID：453 850 0147
时间(Time)：2023年3月31日(周五), 10:30-11:30
邀请人(Inviter)：王灯山
报告摘要
In this talk, in the framework of bidifferential calculus, we investigate the Manakov system via a matrix version of the binary Darboux transformation which involves a Lyapunov equation. With a spectral matrix of the form of diagonal and vanishing seed solutions, the corresponding matrix solution of the Lyapunov equation is given, which can contain zero entries, which should be helpful for further explorations of the solutions of equations with this method. From vanishing and nonvanishing seed solutions, abundant soliton solutions are provided corresponding to a spectral matrix of the form of a Jordan block. In particular, based on the properties of nilpotent matrices, we construct the semirational rogue wave solutions, which can demonstrate the coexistence of rational rogue wave and bright/dark soliton.
主讲人简介
张翼，浙江师范大学数学科学学院教授，博士生导师，浙江师范大学动力系统与非线性中心主任。浙江省应用数学研究会副监事长；中国优选法统筹法与经济数学研究会理事；国家科学技术奖自然科学奖以及多个省市自然科学奖评审专家；科技部数学专项、教育部学位中心评审专家。主要研究方向为孤立子理论与可积系统。曾在美国南佛罗里达大学、阿拉巴马大学，香港中文大学等多所大学访问。主持过多项国家自然科学基金项目及浙江省自然科学基金研究项目；获得过浙江省科学技术一等奖和浙江省人民政府优秀教学成果二等奖。在SCI 源刊杂志上发表论文100余篇。
