Geodesic
On the Fourth Painlevé Hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 101-109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We use the inverse monodromy transform to find the fourth Painlevé hierarchy. The second and third members of this hierarchy are given. Special and rational solutions of the second and third members for the $P_4$ hierarchy are discussed. We apply the Painlevé test to the second member of the fourth Painlevé hierarchy.
Keywords: fourth Painlevé hierarchy, fourth Painlevé equation, special and rational solutions.
Mots-clés : Painlevé test 
@article{TMF_2003_134_1_a8,
     author = {N. A. Kudryashov},
     title = {On the {Fourth} {Painlev\'e} {Hierarchy}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {101--109},
     year = {2003},
     volume = {134},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a8/}
}
TY  - JOUR
AU  - N. A. Kudryashov
TI  - On the Fourth Painlevé Hierarchy
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 101
EP  - 109
VL  - 134
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a8/
LA  - ru
ID  - TMF_2003_134_1_a8
ER  - 
%0 Journal Article
%A N. A. Kudryashov
%T On the Fourth Painlevé Hierarchy
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 101-109
%V 134
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a8/
%G ru
%F TMF_2003_134_1_a8
N. A. Kudryashov. On the Fourth Painlevé Hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 101-109. http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a8/

[1] R. Conte, “The Painlevé approach to nonlinear ordinary differential equations”, The Painlevé Property, One Century Later, CRM Series in Mathematical Physics, ed. R. Conte, Springer, Berlin, 1999, 77 | MR | Zbl

[2] M. J. Ablowitz, H. Segur, Phys. Rev. Lett., 33 (1977), 1103 ; M. J. Ablowitz, A. Ramani, H. Segur, Lett. Nuovo Cimento, 23 (1978), 333 ; J. Math. Phys., 21 (1980), 715 ; 1006 | DOI | MR | DOI | MR | DOI | MR | Zbl | Zbl

[3] M. J. Ablowitz, P. A. Clarkson, Solitons, Nonlinear Evolution Equation and Inverse Scattering, Cambridge Univ. Press, Cambridge, 1991 | MR | Zbl

[4] N. A. Kudryashov, Phys. Lett. A, 224 (1997), 353 ; 252 (1999), 173 ; P. R. Gordoa, A. Pickering, J. Math. Phys., 40 (1999), 5749 ; U. Mugan, F. Jrad, J. Nonlinear Math. Phys., 9 (2002), 282 ; J. Phys. A, 32 (1999), 7933 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[5] P. D. Lax, Commun. Pure Appl. Math., 21 (1968), 467 ; M. J. Ablowitz, D. J. Kaup, A. C. Newell, H. Segur, Stud. Appl. Math., 53 (1974), 249 | DOI | MR | Zbl | DOI | MR | Zbl

[6] V. E. Adler, A. B. Shabat, R. I. Yamilov, TMF, 125:3 (2000), 355 | DOI | MR | Zbl

[7] V. I. Gromak, N. A. Lukashevich, Analiticheskie svoistva reshenii uravnenii Penleve, Universitetskoe, Minsk, 1990 | MR | Zbl

[8] A. Hone, J. Phys. A, 34 (2001), 2235 | DOI | MR | Zbl