Luiz Gustavo Farah

On the periodic Schrödinger–Boussinesq system

Abstract We study the local and global well-posedness of the periodic boundary value problem for the nonlinear Schrodinger–Boussinesq system. The existence of periodic traveling-wave solutions as well as the orbital stability of such solutions are also considered.

Global rough solutions to the cubic nonlinear Boussinesq equation

We prove that the initial value problem for the cubic defocusing nonlinear Boussinesq equation utt - uxx + uxxxx - (|u|2u)xx = 0 on the real line is globally well-posed in Hs(R) provided 2/3 < s < 1.

Large data scattering for the defocusing supercritical generalized KdV equation

ABSTRACT We consider the defocusing supercritical generalized Korteweg–de Vries (gKdV) equation , where k>4 is an even integer number. We show that if the initial data u0 belongs to H1 then the corresponding solution is global and scatters in H1. Our method of proof is inspired on the compactness method introduced by Kenig and Merle.

On the wave operator for the generalized Boussinesq equation

We study the asymptotic behavior of solutions for the generalized Boussinesq equation in a singular framework. We construct a wave operator (inverse scattering) for large profiles ~h belonging to an infinite mass framework based on weak-L spaces. Our solutions converge towards the prescribed scattering state with a polynomial rate. 2000 MSC: 35Q35, 35Q55, 35P25, 35B40, 35L15, 42B35