主题9️⃣：On a special two-dimensional lattice by Blaszak and Szum: matrix integral solutions and solitons
时间🪧：2023年4月20号 10:00-11:30
地点👦🏼： 腾讯会议🧘🏻♂️：662-376-168
主讲人简介：
虞国富🧓🏽，2007年6月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。现为上海交通大学数学科学学院教授、博士生导师，副院长。主要从事孤立子与可积系统🤷🏿♂️、特殊函数🧑🏼✈️、正交多项式方面的研究🤵🏻♂️。在国外重要学术刊物上发表SCI论文50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🚈🪔。
讲座简介：
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 illustrated and analyzed.
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