Geodesic
Modulation instability of soliton trains in fiber communication systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 222-236 
E. A. Kuznetsov; M. D. Spector. Modulation instability of soliton trains in fiber communication systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 222-236. http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a3/
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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.

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