Geodesic
Fermions on a Riemann surface and the Kadomtsev–Petviashvili equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 2, pp. 234-247 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the scattering matrix for free massless fermions on a Riemann surface of finite genus generates the quasiperiodic solutions of the Kadomtsev–Petviashvili equation. The operator changing the genus of the solution is constructed and the composition law of such operators is discussed. The construction extends the well-known operator approach in the case of soliton solutions to the general case of the quasiperiodic $\tau$-functions. 
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     author = {A. V. Zabrodin},
     title = {Fermions {on~a~Riemann} surface and the {Kadomtsev{\textendash}Petviashvili} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. V. Zabrodin. Fermions on a Riemann surface and the Kadomtsev–Petviashvili equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 2, pp. 234-247. http://geodesic.mathdoc.fr/item/TMF_1989_78_2_a6/

[1] Krichever I. M., Novikov S. P., Funkts. analiz i ego prilozh., 21:2 (1987), 46–63 | MR | Zbl

[2] Alvarez-Gaume L., Gomes C., Reina C., Preprint CERN-TH. 4661/87

[3] Krichever I. M., Funkts. analiz i ego prilozh., 11:1 (1977), 15–31 | MR | Zbl

[4] Shiota T., Invent. Math., 83 (1986), 333–382 | DOI | MR | Zbl

[5] Hirota R., Lect. Notes in Math., 515, 1976, 40–68 | DOI | MR | Zbl

[6] Jimbo M., Miwa T., Vertex Operators in Mathematics and Physics, Springer-Verlag, Berlin–Geidelberg–New-York, 1984, 275–290 | MR

[7] Date E., Jimbo M., Kashivara M., Miwa T., Nonlinear integrable systems—classical theory and quantum theory, Proceedings RIMS symp. (Kyoto, 1981), World Scientific, 1983, 39–119 | MR

[8] Friedan D., Shencer S., Nucl. Phys., B281 (1987), 509–545 | DOI | MR

[9] De Vitt B. S., Chernye dyry, Mir, M., 1978, 66–168

[10] Sato M., Dzimbo M., Miva T., Golonomnye kvantovye polya, Mir, M., 1983 | MR

[11] Frenkel I. B., Lect. Notes in Math., 933, 1982 | MR | Zbl

[12] Segal G., Wilson G., Publications IHES, 61, 1985, 5–65 | DOI | Zbl

[13] Morozov A. Yu., Preprint ITEP 87-51, ITEP, M., 1987 | MR

[14] Dubrovin B. A., UMN, 36:2 (1981), 11–80 | MR | Zbl

[15] Klemens G., Mozaika teorii kompleksnykh krivykh, Mir, M., 1984 | MR

[16] Mumford D., Tata Lectures in Theta, Vol. 1, 2, Birchauzer, Boston, 1984 | MR | Zbl

[17] Fay J., Lect. Notes in Math., 352, 1973 | DOI | MR | Zbl

[18] Sonoda H., Phys. Lett., B178 (1986), 390–394 | DOI | MR

[19] A. Besse (red.), Chetyrekhmernaya rimanova geometriya, Mir, M., 1985 | MR

[20] Ishibashi M., Matsuo Y., Ooguri H., Preprint UT-499, Tokyo University, 1986 | Zbl