Time: 9h30, Tuesday, February 10, 2015
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: The 1-d cubic nonlinear Schr\o''dinger equation (NLS) has a special solution called isolated soliton $e^{it} frac{sqrt(2)}{ cosh x}$. There are many results about the nonlinear stability or instability of this solution for 1-d or 2-d cubic nonlinear Schr\o''dinger equation. Otherwise, Davey-Stewartson system (DS) is a two dimensional perturbation of 1-d cubic nonlinear Schro\''dinger equation, so it is interested to study the nonlinear (in-)stability of this soliton under time evolution of this two dimensional model. In this talk, i will present some known results about Davey-Stewartson system, nonlinear (in-)stability of the isolated soliton and discuss some open questions.