报告地点：行健楼学术活动室665
邀请人：张英楠副教授
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.
