Asymptotic solitons of solution of the Korteveg–de Vries equation in the neighbourhood of back front
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 3, pp. 199-212
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_3_a0,
author = {V. B. Baranetskii},
title = {Asymptotic solitons of solution of the {Korteveg{\textendash}de~Vries} equation in the neighbourhood of back front},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {199--212},
year = {1999},
volume = {6},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a0/}
}
TY - JOUR AU - V. B. Baranetskii TI - Asymptotic solitons of solution of the Korteveg–de Vries equation in the neighbourhood of back front JO - Žurnal matematičeskoj fiziki, analiza, geometrii PY - 1999 SP - 199 EP - 212 VL - 6 IS - 3 UR - http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a0/ LA - ru ID - JMAG_1999_6_3_a0 ER -
%0 Journal Article %A V. B. Baranetskii %T Asymptotic solitons of solution of the Korteveg–de Vries equation in the neighbourhood of back front %J Žurnal matematičeskoj fiziki, analiza, geometrii %D 1999 %P 199-212 %V 6 %N 3 %U http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a0/ %G ru %F JMAG_1999_6_3_a0
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) no. 3, pp. 199-212. http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a0/