Orbital stability of a chain of solitons for general nonlinear Schrödinger equations (Jordan Berthoumieu)

We consider travelling waves solutions for a general nonlinear Schrödinger equation. We will study the orbital stability of a chain of travelling waves which speeds are ordered and taken close to the speed of sound $c_s$. The presentation aims at understanding this method which relies on the one used by F. Béthuel, P. Gravejat and D. Smets to prove this result in the case of the Gross-Pitaevskii case and first introduced by Y. Martel, F. Merle and T.-P. Tsai.