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.


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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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