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Modulation instability of soliton trains in fiber communication systems
Authors:E A Kuznetsov  M D Spector
Institution:(1) Landau Institute for Theoretical Physics, Kosygin 2, 117334 Moscow, Russia;(2) Department of Applied Mathematics, Colorado University in Boulder, Boulder, CO, USA
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 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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