Geodesic
Asymptotic solitons of solution of the Korteveg--de~Vries equation in the neighbourhood of back front
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 199-212.

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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. 
@article{JMAG_1999_6_a0,
     author = {V. B. Baranetskii},
     title = {Asymptotic solitons of solution of the {Korteveg--de~Vries} equation in the neighbourhood of back front},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {199--212},
     publisher = {mathdoc},
     volume = {6},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_a0/}
}
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V. B. Baranetskii. Asymptotic solitons of solution of the Korteveg--de~Vries equation in the neighbourhood of back front. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 199-212. http://geodesic.mathdoc.fr/item/JMAG_1999_6_a0/