Geodesic
The Korteweg-de Vries equation in classes of increasing functions with prescribed asymptotics as $|x|\to\infty$
Sbornik. Mathematics, Tome 50 (1985) no. 1, pp. 125-135

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

The Cauchy problem is considered for the Korteweg–de Vries equation with an increasing initial function admitting an asymptotic expansion in decreasing powers of $x$ as $|x|\to\infty$. It is proved that asymptotic solutions having the form of series in decreasing powers of $x$ differ from the actual solutions by a function $w(x,t)$ smooth in $t$ with values in $S(\mathbf R_x)$. Bibliography: 3 titles. 
@article{SM_1985_50_1_a7,
     author = {I. N. Bondareva},
     title = {The {Korteweg-de} {Vries} equation in classes of increasing functions with prescribed asymptotics as $|x|\to\infty$},
     journal = {Sbornik. Mathematics},
     pages = {125--135},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_50_1_a7/}
}
TY  - JOUR
AU  - I. N. Bondareva
TI  - The Korteweg-de Vries equation in classes of increasing functions with prescribed asymptotics as $|x|\to\infty$
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 125
EP  - 135
VL  - 50
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1985_50_1_a7/
LA  - en
ID  - SM_1985_50_1_a7
ER  - 
%0 Journal Article
%A I. N. Bondareva
%T The Korteweg-de Vries equation in classes of increasing functions with prescribed asymptotics as $|x|\to\infty$
%J Sbornik. Mathematics
%D 1985
%P 125-135
%V 50
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1985_50_1_a7/
%G en
%F SM_1985_50_1_a7
I. N. Bondareva. The Korteweg-de Vries equation in classes of increasing functions with prescribed asymptotics as $|x|\to\infty$. Sbornik. Mathematics, Tome 50 (1985) no. 1, pp. 125-135. http://geodesic.mathdoc.fr/item/SM_1985_50_1_a7/