時 間：2024年1月13日10:00-11:30
地 點🤏🏻：1C207室
報告人🙎🏼♀️：虞國富 教授（上海交通大學）
摘要：Recently, rational solutions of integrable differential equations have attracted much attention. In this talk, we will first present a review on the application of Hirota's bilinear method in the construction of rational and semi-rational solutions of integrable equations. Then we investigate a special two-dimensional lattice equation proposed by Blaszak and Szum and so-called Leznov lattice equation based on Hirota's bilinear method. We derive solitons, breathers and rational solutions to the lattice equations both on the constant and periodic backgrounds. These solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. We show that rational solutions can also be presented in terms of Schur polynomials. We demonstrate that these rational solutions exhibit algebraic solitons and lump solitons. We explore the asymptotic analysis to the algebraic solitons.
報告人簡介：虞國富，上海交通大學數學科學EON4教授、博士生導師。2007年博士畢業於中國科EON4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🫚👰🏼、隨機矩陣、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余篇🤣🙍🏼。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✸🍢。
歡迎廣大師生參加！