Geodesic
Hydrodynamic Reductions and Solutions of a Universal Hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 216-229 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We investigate the diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains and analyze their compatibility with previously introduced reductions of differential type.
Keywords: hydrodynamic systems, differential reductions
Mots-clés : hodograph solutions. 
@article{TMF_2004_140_2_a1,
     author = {L. Mart{\'\i}nez Alonso and A. B. Shabat},
     title = {Hydrodynamic {Reductions} and {Solutions} of {a~Universal} {Hierarchy}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {216--229},
     year = {2004},
     volume = {140},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a1/}
}
TY  - JOUR
AU  - L. Martínez Alonso
AU  - A. B. Shabat
TI  - Hydrodynamic Reductions and Solutions of a Universal Hierarchy
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2004
SP  - 216
EP  - 229
VL  - 140
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a1/
LA  - ru
ID  - TMF_2004_140_2_a1
ER  - 
%0 Journal Article
%A L. Martínez Alonso
%A A. B. Shabat
%T Hydrodynamic Reductions and Solutions of a Universal Hierarchy
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2004
%P 216-229
%V 140
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a1/
%G ru
%F TMF_2004_140_2_a1
L. Martínez Alonso; A. B. Shabat. Hydrodynamic Reductions and Solutions of a Universal Hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 216-229. http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a1/

[1] L. Martínez Alonso, A. B. Shabat, Phys. Lett. A, 300 (2002), 58 | DOI | MR | Zbl

[2] L. Martínez Alonso, A. B. Shabat, J. Nonlinear Math. Phys., 10:2 (2003), 229 ; “On the prolongation of a hierarchy of hydrodynamic chains”, New Trends in Integrability and Partial Solvability, Proc. of NATO Adv. Res. Workshop (Cadiz, Spain, 12–16 June 2002), NATO Sci. Ser., 132, eds. A B. Shabat et al., Kluwer, Dordrecht, 2004, 263 | DOI | MR | Zbl | MR | Zbl

[3] A. B. Shabat, TMF, 136:2 (2003), 197 | DOI | MR | Zbl

[4] V. G. Mikhalev, Funkts. analiz i ego prilozh., 26:2 (1992), 79 | MR | Zbl

[5] M. Jaulent, I. Miodek, Lett. Math. Phys., 1 (1976), 243 ; Lett. Nuovo Cimento, 20 (1977), 655 ; L. Martínez Alonso, J. Math. Phys., 21 (1980), 2342 ; M. Antonowicz, A. P. Fordy, Physica D, 28 (1987), 345 ; A. N. W. Hone, Phys. Lett. A, 249 (1998), 46 | DOI | MR | Zbl | DOI | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[6] R. Camassa, D. Holm, Phys. Rev. Lett., 71 (1993), 1661 | DOI | MR | Zbl

[7] J. Gibbons, Y. Kodama, Phys. Lett. A, 135 (1989), 167 ; J. Gibbons, S. P. Tsarev, Phys. Lett. A, 211 (1996), 19 ; 258 (1999), 263 ; M. Mañas, L. Martínez Alonso, E. Medina, J. Phys. A, 35 (2002), 401 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[8] E. V. Ferapontov, K. R. Khusnutdinova, On integrability of $(2+1)$-dimensional quasilinear systems, E-print nlin.SI/0305044

[9] M. V. Pavlov, Integrable hydrodynamic chains, E-print nlin.SI/0301010 | MR

[10] S. P. Tsarev, Izv. AN SSSR. Ser. matem., 54:5 (1990), 1048 | MR | Zbl