Geodesic
Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 46-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. On the moduli space of algebraic Riemann surfaces, we construct flows that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.
Keywords: isoperiodic deformation, periodic acoustic operator, finite-gap solution, integrable system. 
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D. V. Zakharov. Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 46-57. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a3/

[1] E. I. Dinaburg, Ya. G. Sinai, Funkts. analiz i ego prilozh., 9:4 (1975), 8–21 | MR | Zbl

[2] V. A. Marchenko, I. V. Ostrovskii, Matem. sb., 97:4 (1975), 540–606 | MR | Zbl

[3] P. G. Grinevich, M. U. Schmidt, Phys. D, 87:1–4 (1995), 73–98 | DOI | MR | Zbl

[4] N. M. Ercolani, M. G. Forest, D. W. McLaughlin, A. Sinha, J. Nonlinear Sci., 3:1 (1993), 393–426 | DOI | MR | Zbl

[5] I. M. Krichever, Comm. Pure Appl. Math., 47:4 (1994), 437–475 | DOI | MR | Zbl

[6] L. A. Dmitrieva, J. Phys. A, 26 (1993), 6005–6020 | DOI | MR | Zbl

[7] L. A. Dmitrieva, Phys. Lett. A, 182:1 (1993), 65–70 | DOI | MR

[8] L. A. Dmitrieva, D. A. Pyatkin, Phys. Lett. A, 303:1 (2002), 37–44 | DOI | MR | Zbl

[9] C. Rogers, M. C. Nucci, Phys. Scripta, 33:4 (1986), 289–292 | DOI | MR | Zbl

[10] S. Tanveer, Philos. Trans. Roy. Soc. London Ser. A, 343 (1993), 155–204 | DOI | MR | Zbl

[11] H. Knörrer, J. Reine Angew. Math., 334 (1982), 69–78 | MR | Zbl

[12] J. Moser, “Various aspects of integrable Hamiltonian systems”, Dynamical Systems, C.I.M.E. Summer School (Bressanone, 1978), Progr. Math., 8, eds. J. Guckenheimer, J. Moser, Sh. E. Newhouse, Birkhäuser, Boston, 1980, 233–289 | MR | Zbl

[13] A. P. Veselov, Funkts. analiz i ego prilozh., 14:1 (1980), 48–50 | MR | Zbl

[14] A. P. Veselov, Funkts. analiz i ego prilozh., 26:3 (1992), 74–76 | DOI | MR | Zbl

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