Geodesic
Generalized Lamb ansatz
Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 2, pp. 271-282 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the equation $\varphi_{xx}-\varphi_{tt}=\sin\varphi$, a class of 2-phase solutions is constructed. They can be expressed in terms of Jacobi theta functions and contain the Lamb ansatz as a special case. An analogous class of solutions can also be obtained for other integrable nonlinear equations that admit solutions in terms of Riemaan theta functions. 
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E. D. Belokolos; V. Z. Ènol'skii. Generalized Lamb ansatz. Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 2, pp. 271-282. http://geodesic.mathdoc.fr/item/TMF_1982_53_2_a8/

[1] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980, 320 pp. | MR

[2] Lamb G. L., Jr., Rev. Mod. Phys., 43:2 (1971), 99-1-24 | DOI | MR

[3] Kozel V. A., “Ob odnom klasse reshenii uravneniya «Sine-Gordon»”, Voprosy matematicheskoi fiziki i funktsionalnogo analiza, Sb., Naukova dumka, Kiev, 1976, 132–139 | MR

[4] Kozel V. A., Kotlyarov V. P., DAN USSR, ser. A, 1976, no. 10, 878–881 | MR | Zbl

[5] Kozel V. A., Kotlyarov V. P., Differentsialnye uravneniya i nekotorye metody funktsionalnogo analiza, Sb., Naukova dumka, Kiev, 1978, 89–103

[6] Matveev V. B., Abelian Functions and Solitons, Preprint No 373, University of Wroclaw, 1976

[7] Eraser A., Theorie der zweifach unendlichen Thetareihen, Inaugural - Dissertation, Teubner, Leipzig, 1881

[8] Forest G., McLaughlin D. W., Spectral Theory for the Periodic Sine-Gordon Equation: a Concrete View Point, Preprint of Los Alamos Scientific Lab., 1979 | MR | Zbl

[9] Cherednik I. V., DAN SSSR, 252:5 (1980), 1104–1108 | MR | Zbl

[10] Belokolos E. D., Enol'skii V. Z., Classification of Non-Linear Waves in a Josephson Junction, Preprint ITP-81-121 E, ITP, Kiev, 1981

[11] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977, 622 pp. | MR

[12] Dubrovin B. A., DAN SSSR, 251:3 (1980), 541–544 | MR

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

[14] Griffith P., Harris J., Principles of Algebraic Geometry, Wiley. Intersci. Publ., 1978 | MR | Zbl

[15] Zagrodzinski J., Lett. Nuovo Cim., 30:9 (1981), 266–268 | DOI | MR

[16] Krazer A., Lehrbuch der Thetafunktionen, Teubner, Leipzig, 1903, s. 509 | MR | Zbl

[17] Farkas H. M., Kra I., Riemann surfaces, Springer-Verlag, New York, Heidelberg, Berlin, 1980, p. 337 | MR

[18] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, t. 3, Nauka, M., 1967, 299 pp. | MR

[19] Costabile G., Parmentier R. D., Savo B., McLaughlin D. W., Scott A. C., Appl. Phys. Lett., 32 (1978), 587–589 | DOI

[20] Novikov S. P., Funkts. analiz, 8:3 (1974), 54–66 | MR | Zbl

[21] Dubrovin B. A., Novikov S. P., ZhETF, 67:6 (1974), 2131–2143 | MR

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

[23] Belokolos E. D., Enolskii V. Z., UMN, 37:4 (1982), 89

[24] Belokolos E. D., Enol'skii V. Z., On the Solutions Expressed in Terms of Elliptic Functions of the Nonlinear Equations Integrable Within the Inverse Scattering Method and the Reduction Problem of Hyperelliptic Integrals, Preprint ITP-82-36E, ITP, Kiev, 1982 | MR

[25] Dubrovin B. A., Natanzon S. M., Funkts. analiz, 16:1 (1982), 27–43 | MR | Zbl

[26] Forest G., McLaughlin D., Modulations of Sinn-Gordon and Sine-Gordon Wavetrains, Preprint, N.-Y. Univ., N.-Y., 1981 | MR

[27] Date E., Osaka J. Math., 19:1 (1982), 125–158 | MR | Zbl