报告题目 (Title)：The application of Hirota's bilinear method in the construction of rational and semi-rational solutions of integrable equations （Hirota双线性方法在构造可积系统有理解与半有理解中的应用）

报告人 (Speaker)：虞国富 教授（上海交通大学）

报告时间 (Time)：2023年11月02日 15:00-17:30

报告地点 (Place)：校本部D204

邀请人(Inviter)：张大军 教授

主办部门：理学院数学系

报告摘要：

In this talk, we will present some review of the application of Hirota's bilinear method in the construction of rational and semi-rational solutions of integrbale equations. We investigate a special two-dimensional lattice equation proposed by Blaszak and Szum and so-called Leznov lattice based on the Hirota's bilinear method. We derive solitons, breathers and rational solutions to the lattice equations both on the constant and periodic background. These solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. We show that rational solutions are given in terms of Schur polynomials and demonstrate that these rational solutions exhibit algebraic solitons and lump solitons. We explore the asymptotic analysis to the algebraic solitons.