Rational and semi-rational solutions of integrable differential-difference equations


时    间:2024年1月13日10:00-11:30
地    点:1C207室
报告人:虞国富 教授(上海交通大学)

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.

报告人简介:虞国富,上海交通大学数学科学学院教授、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、特殊函数等方面的研究。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60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。