Geodesic
The Bi-Hamiltonian Theory of the Harry Dym Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 311-326

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

We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg–de Vries equation and other soliton equations. This is achieved using a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev–Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such a system the HD–KP hierarchy. We then construct an infinite system of ordinary differential equations (in infinitely many variables) that is equivalent to the HD–KP hierarchy. Its role is analogous to the role of the Central System in the Kadomtsev–Petviashivili hierarchy.
Keywords: $bi$-Hamiltonian formalism, Harry Dym equation, completely integrable systems. 
@article{TMF_2002_133_2_a15,
     author = {M. Pedroni and V. Sciacca and J. P. Zubelli},
     title = {The {Bi-Hamiltonian} {Theory} of the {Harry} {Dym} {Equation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {311--326},
     publisher = {mathdoc},
     volume = {133},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a15/}
}
TY  - JOUR
AU  - M. Pedroni
AU  - V. Sciacca
AU  - J. P. Zubelli
TI  - The Bi-Hamiltonian Theory of the Harry Dym Equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 311
EP  - 326
VL  - 133
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a15/
LA  - ru
ID  - TMF_2002_133_2_a15
ER  - 
%0 Journal Article
%A M. Pedroni
%A V. Sciacca
%A J. P. Zubelli
%T The Bi-Hamiltonian Theory of the Harry Dym Equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 311-326
%V 133
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a15/
%G ru
%F TMF_2002_133_2_a15
M. Pedroni; V. Sciacca; J. P. Zubelli. The Bi-Hamiltonian Theory of the Harry Dym Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 311-326. http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a15/