江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：The application of Hirota's bilinear method in the construction of rational and semi-rational solutions of integrable equations
報告人：虞國富，上海交通大學教授、博士生導師
報告時間：2023年 12月 12日15:00-16:00
騰訊會議：會議 ID： 539-524-8472
報告摘要：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.
專家簡介：虞國富，上海交通大學數學科學學院教授、博士生導師。2007年博士畢業于中國科學院數學與系統科學研究院，加拿大蒙特利爾大學博士後，香港科技大學訪問學者。主要從事可積系統、随機矩陣、正交多項式、特殊函數等方面的研究。在數學物理領域知名學術刊物Adv.Math., Ann. Henri Poincaré，Nonlinearity, JNS等發表SCI論文60餘篇。主持國家自然科學基金、上海市晨光計劃、上海交通大學晨星青年學者獎勵計劃等多項研究課題。