Modulation instability of soliton trains in fiber communication systems

The linear stability problem for a soliton train described by the nonlinear Schrodinger equation is exactly solved using a linearization of the Zakhar ov-Shabat dressing procedure. This problem is reduced to finding a compatib le solution of two linear equations. This approach allows the growth rate o f the soliton lattice instability and the corresponding eigenfunctions to b e found explicitly in a purely algebraic way. The growth rate can be expres sed in terms of elliptic functions. Analysis of the dispersion relations an d eigenfunctions shows that the solution, which has the form of a soliton t rain, is stable for defocusing media and unstable for focusing media with a rbitrary parameters. Possible applications of the stability results to fibe r communication systems are discussed.