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Long time asymptotics for the short pulse equation
时间  Datetime
2018-05-24 14:00 — 15:00 
地点  Venue
1106, Math Building
报告人  Speaker
徐建
单位  Affiliation
上海理工大学
邀请人  Host
Guofu Yu
报告摘要  Abstract

In this paper, we analyze the long-time behavior of the solution of the initial value problem (IVP) for the short pulse (SP) equation. As the SP equation is a completely integrable system, which posses a Wadati-Konno-Ichikawa (WKI)-type Lax pair, we formulate a $2\times 2$ matrix Riemann-Hilbert problem to this IVP by using the inverse scattering method. Since the spectral variable $k$ is the same order in the WKI-type Lax pair, we construct the solution of this IVP parametrically in the new scale $(y,t)$, whereas the original scale $(x,t)$ is given in terms of functions in the new scale, in terms of the solution of this Riemann-Hilbert problem. However, by employing the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann-Hilbert problems, we can get the explicit leading order asymptotic of the solution of the short pulse equation in the original scale $(x,t)$ as time $t$ goes to infinity.