On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation

In this paper, we consider the Cauchy problem for the focusing modified Korteweg-de Vries (mKdV) equation with a weighted Sobolev initial data u(0) is an element of H-2(R)boolean AND L-2,L-s(R), s > 1/2. We use the inverse scattering transform, the dressing -up transformation and (partial derivative) over bar -steepest descent method to prove the asymptotic stability of the multi-solitons of the mKdV equation.