  Multi-soliton solutions of the Korteweg-de Vries equation (KdV) are shown to
be globally L2-stable, and asymptotically stable in the sense of Martel-Merle.
The proof is surprisingly simple and combines the Gardner transform, which
links the Gardner and KdV equations, together with the Martel-Merle-Tsai and
Martel-Merle recent results on stability and asymptotic stability in the energy
space, applied this time to the Gardner equation. As a by-product, the results
of Maddocks-Sachs and Merle-Vega are improved in several directions.
