Geodesic
New exact solutions of two-dimensional integrable equations using the~$\bar\partial$-dressing method
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 377-393

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

We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik–Veselov–Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup–Kupershmidt and Sawada–Kotera equations, constructed using the Zakharov–Manakov $\bar\partial$-dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik–Veselov–Novikov equation.
Keywords: Nizhnik–Veselov–Novikov equation, two-dimensional Kaup–Kupershmidt equation, two-dimensional Sawada–Kotera equation, solutions with functional parameters, two-dimensional stationary Schrödinger equation, transparent potential.
Mots-clés : soliton 
@article{TMF_2011_167_3_a4,
     author = {V. G. Dubrovsky and A. V. Topovsky and M. Yu. Basalaev},
     title = {New exact solutions of two-dimensional integrable equations using the~$\bar\partial$-dressing method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {377--393},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a4/}
}
TY  - JOUR
AU  - V. G. Dubrovsky
AU  - A. V. Topovsky
AU  - M. Yu. Basalaev
TI  - New exact solutions of two-dimensional integrable equations using the~$\bar\partial$-dressing method
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 377
EP  - 393
VL  - 167
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a4/
LA  - ru
ID  - TMF_2011_167_3_a4
ER  - 
%0 Journal Article
%A V. G. Dubrovsky
%A A. V. Topovsky
%A M. Yu. Basalaev
%T New exact solutions of two-dimensional integrable equations using the~$\bar\partial$-dressing method
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 377-393
%V 167
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a4/
%G ru
%F TMF_2011_167_3_a4
V. G. Dubrovsky; A. V. Topovsky; M. Yu. Basalaev. New exact solutions of two-dimensional integrable equations using the~$\bar\partial$-dressing method. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 377-393. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a4/