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

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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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     author = {D. V. Zakharov},
     title = {Isoperiodic deformations of the~acoustic operator and periodic solutions of {the~Harry} {Dym} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {46--57},
     publisher = {mathdoc},
     volume = {153},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a3/}
}
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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/