Asymptotic solitons of solution of the Korteveg–de Vries equation in the neighbourhood of back front

The long time asymptotic behavior of the Cauchy problem solution of the Korteweg–de Vries equation with reflectionless nondecreasing initial data is studied. The data is assumed to be vanishing as $x\to-\infty$ and tend to a periodic function as $x\to+\infty$. It is shown that in a neighbourhood of the back front this solution splits in the infinite series of slow asymptotic solitons as $t\to\infty$. The explicit formulae which describe this phenomenon are obtained.