»ã±¨±êÌâ (Title)£º·ÇÁã²¼¾°Ï¾۽¹NLS·½³Ì£ºÔÚÁ½¸ö¹ý¶ÉÇøÓòϵÄPainleve½¥½ü£¨Defocusing NLS equation with a nonzero background: Painleve asymptotics in two transition regions£©

»ã±¨ÈË (Speaker)£º·¶¶÷¹ó ½ÌÊÚ£¨¸´µ©´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê10ÔÂ16ÈÕ(ÖÜÒ») 14:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÏÄÌú³É ½ÌÊÚ

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»ã±¨ÌáÒª£ºWe address the Painleve asymptotics of the solution in two transition regionsfor the defocusing nonlinear Schrodinger (NLS) equation with finite density initial data. The key to prove this result is the formulation and analysis of a Riemann-Hilbert problem associated with the Cauchy problem for the defocusing NLS equation. With the Dbar generalization of the Deift-Zhou nonlinear steepest descent method and double scaling limit technique, in two transition regions, we find that the leading order approximation to the solution of the defocusing NLS equation can be expressed in terms of the Hastings-McLeod solution of the Painleve II equation in the generic case, while Ablowitz-Segur solution in the non-generic case.