Reflectionless sine-Gordon potentials with an infinite spectrum
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 337-346 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the sine-Gordon $L$-operator, we use dressing chains to construct reflectionless potentials that are self-similar with respect to Darboux transformations. These potentials have an infinite spectrum arranged in a geometric progression. We use numerical methods to show that these potentials have a localized form with modulated tails.
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A. B. Borisov; S. A. Zykov. Reflectionless sine-Gordon potentials with an infinite spectrum. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 337-346. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a2/

[1] M. M. Nieto, D. R. Truax, Phys. Rev. Lett., 71 (1993), 2843 | DOI | MR | Zbl

[2] S. Yu. Dubov, V. M. Eleonskii, N. E. Kulagin, ZhETF, 102:3(9) (1992), 814 ; S. Yu. Dubov, V. M. Eleonskii, N. E. Kulagin, Chaos, 4(1) (1994), 47 | MR | DOI | MR | Zbl

[3] V. M. Eleonskii, V. G. Korolev, ZhETF, 110:6(12) (1996), 1967

[4] A. Degasperis, A. B. Shabat, TMF, 100:2 (1994), 230 | MR | Zbl

[5] A. P. Veselov, A. B. Shabat, Funkts. analiz. i ego prilozh., 27:2 (1993), 1 | MR | Zbl

[6] M. F. Mors, G. Feshbakh, Metody teoreticheskoi fiziki, T. 1, IL, M., 1958

[7] Kh. Grin, Matrichnaya kvantovaya mekhanika, Mir, M., 1968 | MR

[8] J. Weiss, M. Tabor, G. Carnevale, J. Math. Phys., 24 (1983), 522 | DOI | MR | Zbl

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

[10] R. Dodd, Dzh. Eilbek, Dzh. Gibbon, Kh. Morris, Solitony i nelineinye volnovye uravneniya, Mir, M., 1986 | MR

[11] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Mir, M., 1986 | MR

[12] V. B. Matveev, M. A. Salle, Darboux Transformation and Solitons, Springer-Verlag, Berlin–Heidelberg, 1991 | MR

[13] V. E. Adler, I. T. Habibullin, J. Phys. A, 28 (1995), 6717 | DOI | MR | Zbl

[14] A. B. Shabat, Chastnoe soobschenie

[15] V. Yu. Novokshenov, Physica D, 87 (1995), 109 | DOI | MR | Zbl

[16] A. B. Borisov, S. A. Zykov, TMF, 115:2 (1998), 199 | DOI | MR | Zbl