报告问题 (Title)：The application of Hirota's bilinear method in the construction of rational and semi-rational solutions of integrable equations （Hirota双线性要领在结构可积系统有明确与半有明确中的应用）

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

报告所在 (Place)：校本部D204

约请人(Inviter)：张雄师 教授

主理部分：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.