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2022.9.30,程纪鹏 副教授 中国矿业大学,Modified KP hierarchy and its super extension

“可积系统及其应用”学术报告

 目:

Modified KP hierarchy and its super extension

报告人:

程纪鹏 副教授  中国矿业大学

 要:

In this lecture, I will first give a brief review of the (l-l')-th modified KP (mKP) hierarchy, also known as the discrete KP hierarchy, which can be viewed as the orbits of the Darboux transformations. In particular, the 1st mKP hierarchy is just the mKP hierarchy of the Kupershmidt–Kiso version. BKP and modified BKP hierarchies can be viewed as the sub-hierarchies of the 1st mKP hierarchy. Next, the major content of this lecture is devoted to the super extension of the 1st mKP hierarchy in the Kac-van de Leur construction. After introducing some backgrounds in the super extension of KP theory, we construct the corresponding bilinear equations, rewrite them into the super Hirota bilinear forms, and discuss the Darboux transformations in terms of the superfermions. At last, the bilinear equations by introducing the super wave functions are given, which is hoped to be helpful in the derivation of the Lax structures for the super 1st mKP hierarchy.

 间:

930 星期五 14:00—15:30

 式:

腾讯会议

会议 ID574 416 571

会议密码:0930

专家简介:

程纪鹏,中国矿业大学数学学院副教授,博士生导师。博士毕业于中国科学技术大学数学科学学院,清华大学数学科学系国内访问学者,日本东京大学Kavli数物连携宇宙研究机构国家公派访问学者。研究方向:数学物理与可积系统。目前在Adv. Math., Selecta Math., Int. Math. Res. Not., J. Math. Phys., J Geom. Phys., Sci. China Math.等期刊发表科研论文50余篇。主持国家自然基金面上项目一项。