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
Cet article a éte moissonné depuis la source Math-Net.Ru
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/