Stability and quasi-equidistant propagation of NLS soliton trains

Abstract Using the complex Toda chain we model the asymptotic behavior of the N soliton pulse trains of the nonlinear Schrodinger equation. Stable asymptotic regimes are: (i) asymptotically free propagation of all N solitons; (ii) bound state regime where the N solitons may move quasi-equidistantly (QED); and (iii) various intermediate regimes. Our method allows one to determine analytically the set of initial soliton parameters corresponding to each regime. We list the soliton parameters, which ensure QED propagation of all N solitons since this is important for optical fiber communication.

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