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TMF, 1999, Volume 120, Number 2, Pages 222–236 (Mi tmf771)  

This article is cited in 8 scientific papers (total in 8 papers)

Modulation instability of soliton trains in fiber communication systems

E. A. Kuznetsova, M. D. Spectorb

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b National Center of Atmospheric Research

Abstract: The linear stability problem for a soliton train described by the nonlinear Schrödinger equation is exactly solved using a linearization of the Zakharov–Shabat dressing procedure. This problem is reduced to finding a compatible solution of two linear equations. This approach allows the growth rate of the soliton lattice instability and the corresponding eigenfunctions to be found explicitly in a purely algebraic way. The growth rate can be expressed in terms of elliptic functions. Analysis of the dispersion relations and eigenfunctions shows that the solution, which has the form of a soliton train, is stable for defocusing media and unstable for focusing media with arbitrary parameters. Possible applications of the stability results to fiber communication systems are discussed.

DOI: https://doi.org/10.4213/tmf771

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English version:
Theoretical and Mathematical Physics, 1999, 120:2, 997–1008

Bibliographic databases:

Received: 29.10.1998

Citation: E. A. Kuznetsov, M. D. Spector, “Modulation instability of soliton trains in fiber communication systems”, TMF, 120:2 (1999), 222–236; Theoret. and Math. Phys., 120:2 (1999), 997–1008

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Turitsyn S.K. Bale B.G. Fedoruk M.P., “Dispersion-Managed Solitons in Fibre Systems and Lasers”, Phys. Rep.-Rev. Sec. Phys. Lett., 521:4 (2012), 135–203  crossref  mathscinet  isi  scopus  scopus  scopus
    2. Pinsker F., Berloff N.G., Perez-Garcia V.M., “Nonlinear Quantum Piston for the Controlled Generation of Vortex Rings and Soliton Trains”, Phys. Rev. A, 87:5 (2013), 053624  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus  scopus
    3. Agafontsev D.S., Zakharov V.E., “Integrable turbulence generated from modulational instability of cnoidal waves”, Nonlinearity, 29:11 (2016), 3551–3578  crossref  mathscinet  zmath  isi  elib  scopus
    4. JETP Letters, 105:2 (2017), 125–129  mathnet  crossref  crossref  isi  elib
    5. Biondini G., Mantzavinos D., “Long-Time Asymptotics For the Focusing Nonlinear Schrodinger Equation With Nonzero Boundary Conditions At Infinity and Asymptotic Stage of Modulational Instability”, Commun. Pure Appl. Math., 70:12 (2017), 2300–2365  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Degasperis A., Lombardo S., Sommacal M., “Integrability and Linear Stability of Nonlinear Waves”, J. Nonlinear Sci., 28:4 (2018), 1251–1291  crossref  mathscinet  isi  scopus  scopus  scopus
    7. Gelash A.A., Agafontsev D.S., “Strongly Interacting Soliton Gas and Formation of Rogue Waves”, Phys. Rev. E, 98:4 (2018), 042210  crossref  isi  scopus
    8. Rustem R. Aydagulov, Alexander A. Minakov, “Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis”, SIGMA, 14 (2018), 119, 19 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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