报告问题 (Title)：关于Blaszak和Szum的一个特殊二维晶格：矩阵积剖析和孤子（On a special two-dimensional lattice by Blaszak and Szum: matrix integral solutions and solitons）

报告人 (Speaker)： 虞国富 教授（上海交通大学）

报告时间 (Time)：2023年5月18日(周四) 15:00

报告所在 (Place)：腾讯聚会：296 771 815

约请人(Inviter)：夏铁成 教授

主理部分：理学院数学系

报告摘要：In this talk, we study a special two-dimensional lattice equation proposed by Blaszak and Szum. In the first part, we present matrix integral solutions to the lattice equation and its pfaffianized version. In the second part, we derive solitons, breathers and rational solutions to the lattice equation both on the constant and periodic background. These solutions are given in terms of determinants. In particular, we find three types of breather solutions, including Kuznetsov-Ma breather, Akhmediev breather and general one. By introducing two differential operators applied to the soliton solutions, we obtain rational solutions in terms of Schur polynomials. We demonstrate that rational solutions can exhibit algebraic solitons and lump solitons. By taking higher-order differential operators, we present multiple and higher-order rational solutions. The dynamical behaviors of these obtained solutions are investigated and analyzed with plots.