PDE Seminar (2018/7/27): Center stable manifolds around line solitary waves of Zakharov-Kuznetsov equation

Date
2018-7-27 16:30 - 2018-7-27 18:00
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Yohei Yamazaki (Hiroshima University)
 
We consider the two dimensional Zakharov-Kuznetsov equation on a cylindrical space which is one of a high dimensional generalization of Korteweg-de Vries equation. The orbital and asymptotic stability of the one soliton of Korteweg-de Vries equation on the energy space was proved by Benjamin'72, Pego and Weinstein'92, Mizumachi'01 Martel and Merle'01. We regard the one soliton of Korteweg-de Vries equation as a line solitary wave of Zakharov-Kuznetsov equation on a two dimensional space. In the case of the cylindrical space which has the periodic transverse direction, I showed the stability of the line solitary wave with the traveling speed less than the critical speed and the instability with the traveling speed larger than the critical speed. In this talk, to investigate the behavior of solutions around the unstable line solitary wave, we show the existence of a center stable manifolds around unstable line solitary wave with some traveling speed larger than the critical speed on the cylindrical space.