Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data

We show that solutions of the Korteweg-de Vries equation with reflectionless integrable initial data decompose into a (in general infinite) linear superposition of solitons after long enough time. The proof is based on a representation of reflectionless integrable potentials in terms of solutions to symmetric coupling problems for entire functions.