Theoretical and Mathematical Physics

, Volume 120, Issue 2, pp 997–1008 | Cite as

Modulation instability of soliton trains in fiber communication systems

  • E. A. Kuznetsov
  • M. D. Spector


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 eigerfunctions 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.


Soliton Spectral Parameter Elliptic Function Modulation Instability Dark Soliton 
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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • E. A. Kuznetsov
    • 1
  • M. D. Spector
    • 2
  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.Department of Applied MathematicsColorado University in BoulderBoulderUSA

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