»ã±¨±êÌâ (Title)£º¾Û½¹NLS·½³ÌË«¶¥µã´æ±ÉÈ˵ÄÏ¡ÉÙÎÊÌâµÄ³¤¹¦·òÐÐΪ£¨Long-time behaviors of the focusing nonlinear Schr?dinger equation rarefaction problem in presence of double pole£©

»ã±¨ÈË (Speaker)£ºÍõµÆɽ ½ÌÊÚ£¨±±¾©Ê¦·¶´óѧÊýѧ¿ÆѧѧԺ£©

»ã±¨¹¦·ò (Time)£º2023Äê10ÔÂ17ÈÕ(Öܶþ) 14:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飺213-138-646

Ô¼ÇëÈË(Inviter)£ºÏÄÌú³É

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»ã±¨ÌáÒª£º This paper concerns the long-time behaviors of the focusing nonlinear Schr?dinger equation with two kinds of non-zero boundary conditions. One kind is the rarefaction problem and the other is step-like initial-value problem with vanishing boundary on one side. The analytic region of the reflection coefficient is found by studying the convergence of the Volterra integral equations. All possible locations of double poles associated with the spectral functions are established and five sectors are classified for each non-zero boundary condition, such as the dumbing sector, trapping sector, trapping/waking sector, transmitting/waking sector and transmitting sector. The long-time asymptotic behaviors for each sector are analyzed by Deift-Zhou nonlinear steepest-descent strategy for Riemann-Hilbert problems.