Geodesic
Modulation instability and periodic solutions of the nonlinear Schrödinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 2, pp. 189-194 Cet article a éte moissonné depuis la source Math-Net.Ru

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A very simple exact analytic solution of the nonlinear Schrödinger equation is found in the class of periodic solutions. It describes the time evolution of a wave with constant amplitude on which a small periodic perturbation is superimposed. Expressions are obtained for the evolution of the spectrum of this solution, and these expressions are analyzed qualitatively. It is shown that there exists a certain class of periodic solutions for which the real and imaginary parts are linearly related, and an example of a one-parameter family of such solutions is given. 
@article{TMF_1986_69_2_a2,
     author = {N. N. Akhmediev and V. I. Korneev},
     title = {Modulation instability and periodic solutions of the nonlinear {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {189--194},
     year = {1986},
     volume = {69},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a2/}
}
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N. N. Akhmediev; V. I. Korneev. Modulation instability and periodic solutions of the nonlinear Schrödinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 2, pp. 189-194. http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a2/

[1] Novikov S. P., Solitony, eds. R. Bulaf, F. Kodri, Mir, M., 1983, 348–362 | MR

[2] Its A. R., Kotlyarov V. P., DAN USSR, ser. A, 1976, no. 11, 965–968 | MR | Zbl

[3] Babich M. V., Bobenko A. I., Matveev V. B., Izv. AN SSSR, ser. matem., 49:3 (1985), 511–529 | MR | Zbl

[4] Ma Y. C., Ablowitz M. J., Stud. Appl. Math., 65:2 (1981), 113–158 | DOI | MR | Zbl

[5] Tracy E. R., Chen H. H., Lee Y. C., Phys. Rev. Lett., 53:3 (1984), 218–221 | DOI | MR

[6] Hasegawa A., Opt. Lett., 9:7 (1984), 288–290 | DOI

[7] Anderson D., Lisak M., Opt. Lett., 9:10 (1984), 468–470 | DOI

[8] Bespalov V. I., Talanov V. I., Pisma v ZhETF, 3:9 (1966), 471–475

[9] Landau L. D., Lifshits E. M., Elektrodinamika sploshnykh sred, Nauka, M., 1982 | MR

[10] Yuen G., Leik B., Solitony v deistvii, eds. K. Longrena, E. Skott, Mir, M., 1981, 103–137 | MR

[11] Yuen H. C., Ferguson W. E., Phys. Fluids, 21:8 (1978), 1275–1278 | DOI

[12] Akhmediev N. N., Korneev V. I., Kuzmenko Yu. V., ZhETF, 88:1 (1985), 107–115