Geodesic
Matrix modified Kadomtsev–Petviashvili hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 3, pp. 343-356 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Using the bilinear formalism, we consider multicomponent and matrix Kadomtsev–Petviashvili hierarchies. The main tool is the bilinear identity for the tau function realized as the vacuum expectation value of a Clifford group element composed of multicomponent fermionic operators. We also construct the Baker–Akhiezer functions and obtain auxiliary linear equations that they satisfy.
Keywords: matrix modified Kadomtsev–Petviashvili hierarchy, auxiliary linear problem.
Mots-clés : multicomponent fermion 
@article{TMF_2019_199_3_a0,
     author = {A. V. Zabrodin},
     title = {Matrix modified {Kadomtsev{\textendash}Petviashvili} hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {343--356},
     year = {2019},
     volume = {199},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a0/}
}
TY  - JOUR
AU  - A. V. Zabrodin
TI  - Matrix modified Kadomtsev–Petviashvili hierarchy
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 343
EP  - 356
VL  - 199
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a0/
LA  - ru
ID  - TMF_2019_199_3_a0
ER  - 
%0 Journal Article
%A A. V. Zabrodin
%T Matrix modified Kadomtsev–Petviashvili hierarchy
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 343-356
%V 199
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a0/
%G ru
%F TMF_2019_199_3_a0
A. V. Zabrodin. Matrix modified Kadomtsev–Petviashvili hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 3, pp. 343-356. http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a0/

[1] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, “Operator approach to the Kadomtsev–Petviashvili equation – transformation groups for soliton equations III”, J. Phys. Soc. Japan, 50:11 (1981), 3806–3812 | DOI | MR

[2] V. G. Kac, J. W. van de Leur, “The $n$-component KP hierarchy and representation theory”, Important Developments in Soliton Theory, eds. A. S. Fokas, V. E. Zakharov, Springer, Berlin, 1993, 302–343 | MR | Zbl

[3] L.-P. Teo, “The multicomponent KP hierarchy: differential Fay identities and Lax equations”, J. Phys. A: Math. Theor., 44:22 (2011), 225201, 20 pp., arXiv: 1010.5866 | DOI | MR

[4] K. Takasaki, T. Takebe, “Universal Whitham hierarchy, dispersionless Hirota equations and multicomponent KP hierarchy”, Phys. D, 235:1–2 (2007), 109–125 | DOI | MR

[5] V. E. Zakharov, A. B. Shabat, “Skhema integrirovaniya nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya. I”, Funk. anal. i ego pril., 8:3 (1974), 43–53 | DOI | MR | Zbl

[6] E. Date, M. Kashiwara, M. Jimbo, T. Miwa, “Transformation groups for soliton equations”, Non-linear Integrable Systems – Classical Theory and Quantum Theory (Kyoto, Japan, 13–16 May, 1981), eds. M. Jimbo, T. Miwa, World Sci., Singapore, 1983, 39–119 | MR | Zbl

[7] M. Jimbo, T. Miwa, “Solitons and infinite dimensional Lie algebras”, Publ. Res. Inst. Math. Sci., 19:3 (1983), 943–1001 | DOI | MR

[8] I. M. Krichever, A. V. Zabrodin, “Spinovoe obobschenie modeli Reisenarsa–Shnaidera, neabeleva dvumerizovannaya tsepochka Toda i predstavleniya algebry Sklyanina”, UMN, 50:6(306) (1995), 3–56 | DOI | MR | Zbl

[9] I. Krichever, “Periodicheskaya neabeleva tsepochka Toda i ee dvumernoe obobschenie”, UMN, 36:2(218) (1981), 72–77, Prilozhenie k state: B. A. Dubrovin, “Teta-funktsii i nelineinye uravneniya”, 11–80 | DOI | MR | Zbl