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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 153, Number 1, Pages 46–57
DOI: https://doi.org/10.4213/tmf6120 (Mi tmf6120) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

D. V. Zakharov

Columbia University
Full-text PDF (396 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf6120
Abstract: 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.
Received: 27.12.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 153, Issue 1, Pages 1388–1397
DOI: https://doi.org/10.1007/s11232-007-0122-0
Bibliographic databases:
Language: Russian
Citation: D. V. Zakharov, “Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation”, TMF, 153:1 (2007), 46–57; Theoret. and Math. Phys., 153:1 (2007), 1388–1397
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6120
  • https://www.mathnet.ru/eng/tmf/v153/i1/p46
    • This publication is cited in the following 5 articles:
    1. Fanglan Tan, Lihua Wu, “On the Bäcklund transformation of a generalized Harry Dym type equation”, Wave Motion, 120 (2023), 103162  crossref
    2. G.U. Urazboev, A.K. Babadjanova, T.A. Zhuaspayev, “Integration of the periodic Harry Dym equation with a source”, Wave Motion, 113 (2022), 102970  crossref
    3. Ruslan Matviichuk, “Dynamics and exact solutions of the generalized Harry Dym equation”, PIGC, 12:4 (2020), 50  crossref
    4. Li Zh., “Algebro- Geometric Solutions of the Harry Dym Hierarchy”, Int. J. Nonlinear Sci. Numer. Simul., 18:2 (2017), 129–136  crossref  mathscinet  isi
    5. Abenda S., Grinevich P.G., “Periodic billiard orbits on n-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations”, J Geom Phys, 60:10 (2010), 1617–1633  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:68
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