»ã±¨±êÌâ (Title)£ºAnalysis of IMEX and Time-Splitting Schemes for the Logarithmic Schrodinger Equation (¶ÔÊýѦ¶¨ÚÌ·½³ÌµÄÒþʽ-ÏÔʽºÍ¹¦·ò¸îÁÑÌåʽ·ÖÎö)

»ã±¨ÈË (Speaker)£ºÍõÁ¢Áª ½ÌÊÚ£¨Ð¼ÓÆÂÄÏÑóÀí¹¤´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê5ÔÂ18ÈÕ(ÖÜËÄ) 14£º00-15£º00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿ D106

Ô¼ÇëÈË(Inviter)£ºÀƷ¡¢²ÌÃô

Ö÷°ì²¿ÃÅ£ºÀíѧԺÊýѧϵ

»ã±¨ÌáÒª£ºThe Schrodinger equation with a logarithmic nonlinear term (LogSE): f(u)=u log(|u|^2) exhibits many distinct features and rich dynamics that make it unique among nonlinear wave equations. However, such a nonlinearity presents significant challenges in both numerical solutions and analysis. Compared with usual cubic case, the nonlinear term f(u) is non-differentiable at u=0 but only possesses certain Holder continuity. In this talk, we shall report our recent attempts in numerical study of the LogSE with a focus on time discretization via implicit-explicit scheme and time-splitting scheme and on the introduction of new tools for the error analysis. This talk is based on joint works with Jingye Yan (Jiangsu University) and Xiaolong Zhang (Hunan Normal University).