红楼Y论坛（第六十三讲）-Super modified KP hierarchy in Kac-van de leur construction

红楼Y论坛（第六十三讲）

Topic: Super modified KP hierarchy in Kac-van de leur construction

Time：15:00-16:00 Mar. 15, 2023(Wednesday）

Place：Room457，Haiqin No.2

Speaker：Huizhan Chen

Abstract：In this talk, the modified KP hierarchy in Kupershmidt-Kiso verson is extended to the super case by Kac-van de Leur construction, that is, using highest weight representations of the even part in the tensor product of the infinite-dimensional Lie superalgebra $gl_{\infty|\infty}$ with Grassmann algebra $\mathcal{G}$. Firstly, the super modified KP (SmKP) hierarchy is constructed in terms of superfermionic bilinear equations. Then the superbosonic form of the SmKP hierarchy is given by super boson-fermion correspondence. With the help of super Hirota bilinear operators, the corresponding super Hirota bilinear equations of the SmKP hierarchy are obtained. Next,the Darboux transformations of this new SmKP hierarchy are expressed in the forms of free superfermions and  various solutions are derived. At last, the super bilinear equations in the forms of super wave functions are also constructed from the superbosonic ones, which is hoped to be helpful to obtain the corresponding Lax structures