Stability of nonlinear patterns in low dimensional Bose gases & “Long time existence for some Boussinesq type systems”

Title: Stability of nonlinear patterns in low dimensional Bose gases

Abstract: In this talk I will present recent results, obtained in collaboration with prof. A. Corcho (UFRJ, Brazil), on the rigorous study of the orbital stability properties of the simplest nonlinear pattern in low dimensional Bose gases, the  black soliton solution. This is a solution of a  non-integrable defocusing Schrödinger model, represented by the  quintic Gross-Pitaevskii equation (5GP). Once the black soliton is characterized as a critical point of the associated Ginzburg-Landau energy of the 5GP, I will show some coercivity properties of that energy around the black (and dark) soliton. I will also explain how to impose suitable orthogonality conditions and how to control the growth of some modulation parameters to finally prove that perturbations generated by the symmetries of the 5GP stay close to the black soliton in the energy space.


Title: “Long time existence for some Boussinesq type systems”

Abstract: We establish the long time existence of solutions to the Cauchy problem for two type of Boussinesq systems.

One is a strongly dispersive Boussinesq system whose phases have  a non trivial zero set, necessitating the use of normal forms. The second one  is a class of  “Full Dispersion-Boussinesq” systems arising in the modeling of internal waves in a two-layers system.

Based on joint work with Li Xu.

Date: Nov 27, 2019 at 15:00:00 h
Venue: La Sala de Seminario Felipe Álvarez Daziano, 5to piso, Torre Norte de Beauchef 851.
Speaker: Miguel Angel Alejo & Jean-Claude Saut
Coordinator: Prof. Matteo Rizzi

Posted on Nov 22, 2019 in Differential Equations, Seminars