»ã±¨±êÌâ (Title)£ºThe application of Hirota's bilinear method in the construction of rational and semi-rational solutions of integrable equations £¨HirotaË«ÏßÐÔ²½ÖèÔÚ»ú¹Ø¿É»ýϵͳÓÐÀí½âÓë°ëÓÐÀí½âÖеÄÀûÓã©

»ã±¨ÈË (Speaker)£ºÓݹú¸» ½ÌÊÚ£¨ÉϺ£½»Í¨´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ02ÈÕ 15:00-17:30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿D204

Ô¼ÇëÈË(Inviter)£ºÕÅÐÛʦ ½ÌÊÚ

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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.