Speaker: Pro.Xueke Pu(Guangzhou University)
Title1:On the Euler-Poisson equation for ions
Time: Tues, Nov.20, 2018 , PM:7:30-8:30
Location: Room 4318, Building No.4, Wushan Campus
Speaker: Dr.Qingtang Su (The University of Michigan)
Title2:Long time behavior of 2d water waves with point vortices
Time: Tues, Nov.20, 2018 , PM:8:30-9:30
Location: Room 4318, Building No.4, Wushan Campus
Speaker: Pro.Jinsong He(Ningbo University)
Title3:Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system
Time: Fri, Nov.23, 2018 , PM:4:30-5:30
Location: Room 4318, Building No.4, Wushan Campus
Abstract 1:
In this talk, we will introduce some recent results on the Euler-Poisson equation for ions. In particular, we will consider the derivation of the KdV and the Nonlinear Schrodinger equation from the Euler-Poisson equation and other related limiting problems.
Abstract 2:
In this paper, we study the motion of the two dimensional inviscid incompressible, infinite depth water waves with point vortices in the fluid. We show that Taylor sign condition
can fail if point vortices are sufficient close to the free boundary, so the water waves could be subject to Taylor instability. Assuming Taylor sign condition, we prove that the water wave system is locally well posed in Sobolev spaces. Moreover, we show that if the water waves is symmetric with a symmetric vortex pair traveling downward initially, then the free interface remains smooth for a long time, and for initial data of size
1, the lifespan is at least
. The result can be extended to global and obtained modified scattering for localized initial data.
Abstract 3:
In this talk, we shall show some new semi-rational solutions on an integrable multi-component (2 + 1)-dimensional long-wave-short-wave resonance interaction system, which are obtained by using Hirota method and a special limit. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviors of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission.
The main reference is mainly based on a paper of mine joint with my student Jiguang Rao and two India Professors Kuppuswamy Porsezian, Thambithurai Kanna, (Proc. R. Soc. A 474: 20170627.)
