Geodesic
Whitham hierarchy in growth problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 197-217

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

We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. This equivalence allows distinguishing a class of exact solutions of the Laplacian growth problem in the multiply connected case. These solutions correspond to finite-dimensional reductions of the Whitham hierarchy representable as equations of hydrodynamic type, which are solvable by the generalized hodograph method.
Mots-clés : Saffman–Taylor problem
Keywords: Laplacian growth, Whitham equations, Schwarz function. 
@article{TMF_2005_142_2_a1,
     author = {A. V. Zabrodin},
     title = {Whitham hierarchy in growth problems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {197--217},
     publisher = {mathdoc},
     volume = {142},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a1/}
}
TY  - JOUR
AU  - A. V. Zabrodin
TI  - Whitham hierarchy in growth problems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 197
EP  - 217
VL  - 142
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a1/
LA  - ru
ID  - TMF_2005_142_2_a1
ER  - 
%0 Journal Article
%A A. V. Zabrodin
%T Whitham hierarchy in growth problems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 197-217
%V 142
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a1/
%G ru
%F TMF_2005_142_2_a1
A. V. Zabrodin. Whitham hierarchy in growth problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 197-217. http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a1/