Riemann-Hilbert Approach and Whitham Modulation Theory to Asymptotic Problems of Some Classical Integrable Systems
Time: 2022-09-02
Published By: Wenqiong Li
Speaker(s): Dengshan Wang (Beijing Normal University)
Time: 14:00-15:00 September 6, 2022
Venue: Room 29, Quan Zhai, BICMR
In this talk, we report our recent work on the asymptotic analysis of some classical integrable systems by Riemann-Hilbert approach and Whitham modulation theory. After the introduction, the second part introduces the long-time asymptotic behaviors of two separable plane waves of the focusing NLS equation. The third part focuses on the far-field behaviors of multiple-pole solitons of the focusing NLS equation in the large-order limit. The fourth part reports the long-time asymptotics of the focusing KE equation with nonzero boundary conditions at infinity. Then we report our recent result on the long-time asymptotics of the initial-value problem for the good Boussinesq equation on the line. Finally, the classification of solutions to the integrable equations of NLS type with discontinuous initial data is studied by Whitham modulation theory.
