Geodesic
Universal Models of Soliton Hierarchies
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 197-208 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider commutativity equations and a related new model similar to the Kadomtsev–Petviashvili equation in the Sato theory. Integration of this model equation with three independent variables is based on a generalization of the Dubrovin equations and the recently developed theory of transformations of spectral problems. We give examples of equations with a fractional-power dispersion law that can be linearized in this theory.
Keywords: commutativity equations, classical hierarchies.
Mots-clés : Dubrovin equations 
@article{TMF_2003_136_2_a1,
     author = {A. B. Shabat},
     title = {Universal {Models} of {Soliton} {Hierarchies}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {197--208},
     year = {2003},
     volume = {136},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a1/}
}
TY  - JOUR
AU  - A. B. Shabat
TI  - Universal Models of Soliton Hierarchies
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 197
EP  - 208
VL  - 136
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a1/
LA  - ru
ID  - TMF_2003_136_2_a1
ER  - 
%0 Journal Article
%A A. B. Shabat
%T Universal Models of Soliton Hierarchies
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 197-208
%V 136
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a1/
%G ru
%F TMF_2003_136_2_a1
A. B. Shabat. Universal Models of Soliton Hierarchies. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 197-208. http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a1/

[1] E. Date, M. Jimbo, M. Kajivara, T. Miva, J. Phys. Soc. Japan, 50 (1981), 3806–3812 | DOI | MR | Zbl

[2] N. Kh. Ibragimov, A. B. Shabat, Funkts. analiz i ego prilozh., 14:4 (1980), 79–80 | MR | Zbl

[3] L. Martínez Alonso, A. B. Shabat, Phys. Lett. A, 229 (2002), 359–365; E-print nlin.SI/0202008

[4] L. Martínez Alonso, A. B. Shabat, J. Nonlinear Math. Phys., 10(2) (2003), 229–242 | DOI | MR | Zbl

[5] R. Heredero, A. B. Shabat, V. V. Sokolov, “A new class of linearizible equations”, J. Nonlin. Math. Phys., 2003, Submitted | MR | Zbl

[6] S. I. Svinolupov, UMN, 40:5 (1985), 263–264 | MR | Zbl

[7] V. E. Adler, I. T. Khabibullin, A. B. Shabat, TMF, 110:1 (1997), 98–113 | DOI | MR | Zbl

[8] B. A. Dubrovin, V. B. Matveev, S. P. Novikov, UMN, 31:1 (1976), 55–136 | MR | Zbl

[9] B. L. Rozdestvenskii, A. D. Sidorenko, Comput. Math. Math. Phys., 7 (1967), 1176 | MR

[10] E. Ferapontov, Phys. Lett. A, 158 (1991), 112–118 | DOI | MR