Stability of multi-solitons in the cubic NLS equation

We address the stability of multi-solitons for the cubic nonlinear Schrödinger (NLS) equation on the line. By using the dressing transformation and the inverse scattering transform methods, we establish the orbital stability of multi-solitons in the L 2 (ℝ) space when the initial data is in a weighted L 2 (ℝ) space.