Modulation instability of soliton trains in fiber communication systems

E. A. Kuznetsov, M. D. Spector

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)997-1008
Number of pages12
JournalTheoretical and Mathematical Physics
Volume120
Issue number2
DOIs
Publication statusPublished - Aug 1999
Externally publishedYes

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