(In)stability and asymptotic analysis of the Zakharov-Rubenchik system and related wave type equations
Speaker: Luong Thai Hung

Time: 9h30, Tuesday, Novemer 13, 2018
Location: Room 302 Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: The transverse stability describes the orbital stability of a 1-D solitary wave under the time evolution of a 2-D model, It is a very interesting and also difficult topic in PDE. The nonlinear transverse stability for  a class of PDE was recently studied by Fredric Rousset and Nikolay Tvetzkov, they gave a general method for a large class of equation including the (cubic) nonlinear Schroedinger equation. However, It is nontrivial to extend this method to another class of PDE of Schroedinger type, for example, the transverse stability is still unknown for the Davey-Stewartson system, Zakharov system and Zakharov-Rubenchik system. In this talk, we introduce the transverse stability and our recent results on this problem