报告题目：Solutions of a special two-dimensional lattice by Blaszak and Szum

报告人： 虞国富教授

工作单位：上海交通大学

报告时间：7月14日（周四）14:00-15:00

腾讯会议号：712769405

报告摘要：

In this talk, we study the Blaszak and Szum  lattice equation. We first construct the matrix integral solutions for the lattice equation and its Pfaffianized system. We show that the partition function of the Hermitian matrix model with unitary invariance gives the tau function of the lattice equation. The tau functions of the Pfaffianized system are expressed in terms of the partition function of orthogonal ensemble and  symplectic ensemble, respectively. Solitons, breathers and rational solutions to the lattice equation are derived based on the bilinear Hirota method and KP hierarchy reduction approach.  We show that Schur polynomials are associated to  rational solutions. Considering the effect of the parameter $n$ in lattice equations, we find solutions including algebraic solitons and lump solutions on $(n,y)$-plane. We elucidate explicit expressions of asymptotic algebraic solitons localized in the straight for the algebraic soliton solutions by asymptotic analysis.  

报告人简介：

虞国富，上海交通大学教授、博士生导师。2007年博士毕业于中国科学院数学与系统科学研究院，加拿大蒙特利尔大学博士后。主要从事孤立子与可积系统、特殊函数、正交多项式等方面的研究。在数学物理领域学术刊物上发表SCI论文40余篇。主持国家自然科学基金、上海市晨光计划、上海交通大学晨星青年学者奖励计划等多项研究课题。