﻿2021.2.26,楼森岳 教授，Duality of positive and negative integrable hierarchies via relativistic invariant fields-中国矿业大学（北京）理学院网站

2021.2.26,楼森岳 教授，Duality of positive and negative integrable hierarchies via relativistic invariant fields

 题  目： Duality of positive and negative integrable hierarchies via relativistic invariant fields 报告人： 楼森岳 教授，宁波大学 摘  要： It is shown that the relativistic invariance is very important in the study of integrable systems. Using the relativistic invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual relations, some continuous and discrete integrable positive hierarchies such as the potential modified Korteweg-de Vries hierarchy, the potential Fordy-Gibbons hierarchies, the (2+1)-dimensional potential dispersionless Kadomtsev-Petviashvili like (dKPL) hierarchy, the differential-difference dKPL hierarchy and the heavenly hierarchies are changed to the integrable negative hierarchies including the sG hierarchy and the Tzitzeica hierarchy, the continuous Toda hierarchy, the differential-difference Toda hierarchies and negative heavenly hierarchy. In (1+1)-dimensional cases the positive/negative hierarchy dualities are guaranteed by the dualities between the recursion operators and their inverse operators. In (2+1)-dimensional cases, the positive/negative hierarchy dualities are explicitly shown by using the formal series symmetry approach, the master symmetry method and the relativistic invariance of the duality relations. For the 4-dimensional heavenly system, the duality problem is studied firstly by formal series symmetry approach. Two elegant commuting recursion operators of the heavenly equation are naturally appeared from the formal series symmetry approach such that the duality problem can also be studied by means of the recursion operators. 时  间： 2月26日 星期五 8:30—9:30 方  式： 腾讯会议会议 ID：763 230 915会议密码：0126 邀请人： 刘青平 教授