Geodesic
Interpolating differential reductions of multidimensional integrable hierarchies
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 354-363

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

We apply the scheme for constructing differential reductions recently developed for the Manakov–Santini hierarchy to the general multidimensional case. We consider the four-dimensional case connected with the second heavenly equation and its generalization proposed by Dunajski in more detail. We characterize differential reductions in terms of the Lax–Sato equations and also in the framework of the dressing method based on the nonlinear Riemann–Hilbert problem.
Keywords: multidimensional integrable hierarchy, differential reduction, Plebański equation. 
@article{TMF_2011_167_3_a2,
     author = {L. V. Bogdanov},
     title = {Interpolating differential reductions of multidimensional integrable hierarchies},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {354--363},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a2/}
}
TY  - JOUR
AU  - L. V. Bogdanov
TI  - Interpolating differential reductions of multidimensional integrable hierarchies
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 354
EP  - 363
VL  - 167
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a2/
LA  - ru
ID  - TMF_2011_167_3_a2
ER  - 
%0 Journal Article
%A L. V. Bogdanov
%T Interpolating differential reductions of multidimensional integrable hierarchies
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 354-363
%V 167
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a2/
%G ru
%F TMF_2011_167_3_a2
L. V. Bogdanov. Interpolating differential reductions of multidimensional integrable hierarchies. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 354-363. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a2/