Geodesic
On some set of elliptic solutions of the Boussinesq equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 3, pp. 347-356 Cet article a éte moissonné depuis la source Math-Net.Ru

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An ansatz concerning Krichever curves is considered for two-periodic finite-gap solutions of the Boussinesq equation. These solutions are expressed in terms of equianharmonic elliptic Weierstrass $\wp$-functions. Examples are given. 
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A. O. Smirnov. On some set of elliptic solutions of the Boussinesq equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 3, pp. 347-356. http://geodesic.mathdoc.fr/item/TMF_1996_109_3_a2/

[1] H. Airault, H. P. McKean, J. Moser, Comm. Pure Appl. Math., 30 (1977), 95–148 | DOI | MR | Zbl

[2] I. M. Krichever, Funkts. analiz i ego prilozh., 14:4 (1980), 45–54 | MR | Zbl

[3] A. R. Its, V. Z. Enolskii, Funkts. analiz i ego prilozh., 20:1 (1986), 73–74 | MR | Zbl

[4] B. A. Dubrovin, S. P. Novikov, ZhETF, 67:12 (1974), 2131–2143 | MR

[5] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980 | MR

[6] E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Enolskii, UMN, 41:2 (1986), 3–42 | MR | Zbl

[7] J.-L. Verdier, Algebraic Analisys, Micio Sato Sixtieth Birthday Vol., V. II, Academic Press, 1988, 901–910 | DOI | MR

[8] A. Treibich, Duke Math. J., 59:3 (1989), 611–627 | DOI | MR | Zbl

[9] A. Treibich, J.-L. Verdier, Solitons elliptiques, Volume en l'honneur du $60^e$ anniversaire du prof. A. Grothendieck, Birkhäuser, Boston, 1990 | MR | Zbl

[10] E. D. Belokolos, V. Z. Enolskii, UMN, 44:5 (1989), 155–156 | MR | Zbl

[11] E. D. Belokolos, V. Z. Enolskii, Funkts. analiz i ego prilozh., 23:1 (1989), 57–58 | MR | Zbl

[12] A. O. Smirnov, Mat. zametki, 45:6 (1989), 66–73 | MR | Zbl

[13] E. D. Belokolos, A. I. Bobenko, V. Z. Enol'skii, A. R. Its, V. B. Matveev, Algebro-geometrical approach to nonlinear evolution equations, Springer Ser. Nonlinear Dynamics, Springer, Berlin–Heidelberg–New York, 1994

[14] A. O. Smirnov, Acta Appl. Math., 36 (1994), 125–166 | DOI | MR | Zbl

[15] V. Z. Enol'skii, N. A. Kostov, Acta Appl. Math., 36 (1994), 57–86 | DOI | MR | Zbl

[16] E. D. Belokolos, V. Z. Enol'skii, Acta Appl. Math., 36 (1994), 87–117 | DOI | MR | Zbl

[17] A. I. Bobenko, Funkts. analiz i ego prilozh., 18:3 (1984), 74–75 | MR

[18] A. O. Smirnov, Mat. zametki, 46:5 (1989), 100–102 | MR | Zbl

[19] A. O. Smirnov, Mat. sbornik, 181:6 (1990), 804–812 | Zbl

[20] A. O. Smirnov, TMF, 100:2 (1994), 183–198 | MR | Zbl

[21] A. O. Smirnov, Mat. sbornik, 185:8 (1994), 103–114 | Zbl

[22] A. O. Smirnov, Mat. zametki, 58:1 (1995), 86–97 | MR | Zbl

[23] A. O. Smirnov, Mat. sbornik, 186:8 (1995), 134–141 | MR

[24] V. B. Matveev, A. O. Smirnov, DAN SSSR, 293:1 (1987), 78–82 | MR | Zbl

[25] V. B. Matveev, A. O. Smirnov, Rasprostranenie voln. Teoriya rasseyaniya, Problemy matematicheskoi fiziki, vyp. 12, LGU, L., 1987, 225–236 | MR

[26] V. B. Matveev, A. O. Smirnov, Lett. in Math. Phys., 14 (1987), 25–31 | DOI | MR | Zbl

[27] G. H. Halphen, Mem. pres. l'Acad. de Sci. de France, 28 (1884), 1–300

[28] E. Kamke, Spravochnik po obyknovennym differentsialnym uravneniyam, Fizmatgiz, M., 1961 | MR

[29] V. P. Gerdt, N. A. Kostov, Computers and Mathematics, eds. E. Kaltofen, S. M. Watt, Springer, Berlin–Heidelberg, 1989, 277–283 | MR

[30] J. C. Eilbeck, V. Z. Enolskii, J. Math. Phys., 35:3 (1994), 1192–1201 | DOI | MR | Zbl

[31] Yu. V. Brezhnev, Phys. Lett. A, 211 (1996), 94–100 | DOI | MR | Zbl

[32] I. M. Krichever, DAN SSSR, 227:2 (1976), 291–294 | MR | Zbl

[33] I. M. Krichever, UMN, 32:6 (1977), 180–208

[34] E. I. Zverovich, UMN, 26:1 (1971), 113–179 | MR | Zbl

[35] V. B. Matveev, Abelian functions and solitons, Preprint No 373, Univ. of Wrocław, 1976

[36] A. Hurwitz, Math. Ann., 41 (1893), 403–442 | DOI | MR

[37] F. K. Schmidt, Math. Zeit., 45 (1938), 75–96 | DOI

[38] V. V. Silvestrov, L. I. Chibrikova, Izv. vuzov. Matematika, 1979, no. 12, 51–56 | MR | Zbl

[39] N. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR | Zbl