Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Dengshan Wang, Beijing Normal University
Inviter:	张国强
Title:	Long-time asymptotics for the rarefaction problem of the focusing nonlinear Schrodinger equation in presence of discrete spectrum
Language:	Chinese
Time & Venue:	2023.06.12 16:00-17:00 S625
Abstract:	The long-time asymptotic behaviors of the rarefaction problem for the focusing nonlinear Schr?dinger equation with discrete spectrum are analyzed via the Riemann-Hilbert formulation. Both single pole and double pole of the meromorphic matrix-valued function are considered. It is shown that for the rarefaction problem with pure step initial condition there are three asymptotic sectors in time-space: the plane wave sector, the 1-phase elliptic wave sector and the vacuum sector, while for the rarefaction problem with general initial data there are more than three asymptotic sectors in time-space. The leading-order term of each sector along with the corresponding error estimate are given by adopting the Deift-Zhou nonlinear steepest-descent method for Riemann-Hilbert problems. The asymptotic solutions match very well with the results from Whitham modulation theory and the direct numerical simulations.