Geodesic
On the problem of first correction in soliton perturbation theory
Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 977-1002

Voir la notice de l'article provenant de la source Math-Net.Ru

For an integro-differential equation with rapidly oscillating kernel of Cauchy type it is proved that a solution exists and is uniformly bounded in the Holder norm with respect to a small parameter $\varepsilon$. This equation describes the essential part of the first correction in soliton perturbation theory. An asymptotic estimate is obtained for this correction, which implies that the soliton structure of the solution of an equation close to the integral equation is preserved for times $\sim\varepsilon^{-1}$. 
@article{SM_1995_186_7_a4,
     author = {L. A. Kalyakin},
     title = {On the problem of first correction in soliton perturbation theory},
     journal = {Sbornik. Mathematics},
     pages = {977--1002},
     publisher = {mathdoc},
     volume = {186},
     number = {7},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_7_a4/}
}
TY  - JOUR
AU  - L. A. Kalyakin
TI  - On the problem of first correction in soliton perturbation theory
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 977
EP  - 1002
VL  - 186
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_7_a4/
LA  - en
ID  - SM_1995_186_7_a4
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%T On the problem of first correction in soliton perturbation theory
%J Sbornik. Mathematics
%D 1995
%P 977-1002
%V 186
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1995_186_7_a4/
%G en
%F SM_1995_186_7_a4
L. A. Kalyakin. On the problem of first correction in soliton perturbation theory. Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 977-1002. http://geodesic.mathdoc.fr/item/SM_1995_186_7_a4/