7月3日 胡星标:Nonlocal symmetries for bilinear equations and their applications

来源:pt真人平台 时间:2020-06-25浏览:47设置


讲座题目:Nonlocal symmetries for bilinear equations and their applications

主讲人:胡星标  研究员

主持人:傅蔚

开始来源:pt真人平台 时间:2020-07-03   15:00:00  结束来源:pt真人平台 时间:2020-07-03   16:00:00

讲座地址:腾讯会议  ID338 873 259

主办单位:数学科学学院

 

报告人简介:

       胡星标,中国科学院数学与系统科学研究院研究员,博导。主要研究方向为可积系统与数值算法。现任《应用数学学报》英文版编委,《数学进展》编委,《Journal of Nonlinear Math. Phys.》编委,《Pacific Journal of Appl. Math.》编委。

 

报告内容:

In this talk, nonlocal symmetries for the   bilinear KP and bilinear BKP equations are restudied. Two arbitrary   parameters are introduced in these nonlocal symmetries by considering gauge invariance of the bilinear KP and bilinear BKP equations under a certain  transformation. By expanding these nonlocal symmetries in power series of each of two parameters, we have derived two types of bilinear NKP hierarchies and two types of bilinear NBKP hierarchies. An impressive observation is that bilinear positive and negative KP (NKP) and BKP hierarchies may be derived   from the same nonlocal symmetries for the KP and BKP equations. Besides, as   two concrete examples, we have derived bilinear B?cklund transformations for  t_2flow of the NKP hierarchy and t_{-1}flow of the NBKP hierarchy. All these results have made it clear that more beautiful integrability properties would be found for these obtained NKP   hierarchies and NBKP hierarchies. Because KP and BKP hierarchies have played   an essential role in soliton theory, we believe that the bilinear NKP and   NBKP hierarchies will have their right place in this field.

 


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