报告题目：Getting More Solutions from Solitons: A Limit Approach
报 告 人：张大军（上海大学 教授）
报告时间：2020年11月19日（星期四）13:30开始
报告地点：阳明学院303
报告摘要：This talk focuses on limit solutions of soliton equations. In general, from the viewpoint of the Inverse Scattering Transform, N-solitons are identified by N distinct eigenvalues, or in other words, N distinct simple poles {k_j} of transparent coefficient 1/a(k), (or N simple zeros of Jost solution a(k)). When {k_j} are multipl-poles, the related multipl-pole solution can be obtained by a limit procedure like k_2 à k_1 from simple-pole solution. In the talk we will make a survey on limit solutions from viewpoints of the Inverse Scattering Transform, Darboux transformation, Bäcklund transformation, Hirota's method and Cauchy matrix approach. We discuss simple and compact expressions for the limit solutions, and also describe an exact limit procedure to show how each parameter in a limit solution is exactly derived through the procedure. This procedure is also helpful for investigating dynamics of limit solutions. Besides, we consider new symmetries derived also based on limit ideas and the related new solutions.
报告人简介：张大军，上海大学数学系教授，博士生导师。2002年上海大学获博士学位，先后作为国家公派留学人员和访问学者访问芬兰Turku大学、英国Leeds大学、剑桥牛顿数学研究所、美国Texas大学(RGV)、澳大利亚Sydney大学、La Trobe大学、日本早稻田大学等。2007年破格晋升教授。曾获上海市优秀博士学位论文，上海市高校优秀青年教师。先后主持国家自然科学基金面上项目5项、教育部博士点基金（博导类）1项、参与国家自然科学基金重点项目1项。目前主要研究非线性数学物理中的离散可积系统，长期国际合作单位包括Turku大学、Leeds大学、La Trobe大学等。目前指导博士生10位、硕士生5位。曾担任国际期刊Journal of Nonlinear Mathematical Physics编委(2006-2020)。目前担任国际系列会议SIDE (Symmetries and Integrability of Difference Equations)指导委员会委员(2012--)，国际期刊 Journal of Physics A: Math. Theore.编委（2020--）。
