The trigonometric-type three-field Blaszak-Marciniak lattice equation
数学专题报告
报告题目(Title)：The trigonometric-type three-field Blaszak-Marciniak lattice equation
报告人(Speaker)：虞国富 教授（上海交通大学）
地点(Place)：后主楼1220
时间(Time)：2026年5月31日（周日）10:00-11:00
邀请人(Inviter)：王灯山
报告摘要
In this talk, we propose a novel variant three-field Blaszak-Marciniak (BM) lattice equation by introducing trigonometric-type bilinear operators and leveraging the reduction technique from the variant KP-Toda hierarchy. Applying Hirota's bilinear method, we derive general Gram-type determinant solutions. Rational solutions of the variant BM lattice are obtained via Bäcklund transformation and differential operators method. Higher-order rogue waves are formulated in terms of Schur polynomials, whose peak patterns are linked to the root structures of Yablonskii-Vorob'ev polynomials and Umemura polynomials. Furthermore, three distinct types of breather solutions are identified, and numerical three-periodic wave solutions are computed using the Gauss-Newton method.
主讲人简介
虞国富，上海交通大学数学科学学院教授、副院长、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，香港科技大学访问学者。主要从事可积系统、随机矩阵、正交多项式等方面的研究。在数学物理领域知名学术刊物Adv. Math., Ann. Henri Poincaré，Nonlinearity, JNS等发表SCI论文70余篇。主持国家自然科学基金、上海市东方英才、上海交通大学晨星青年学者奖励计划等多项研究课题。
