arXiv subjects

I. M. Uzunov

Publications and source records attributed to I. M. Uzunov.

2 recordsLinked to original sources

arXiv2000

N-soliton train interactions and perturbed complex Toda chain in nonlinear optics. Adiabatic and non-adiabtic aspects

Our previous results on the N-soliton interaction in the adiabatic approximation have been extended. It is shown that the complex Toda chain (CTC) model is an universal one in the sense that it describes the N-soliton train interactions for all NLEE from the NLS hierarchy. We derive the perturbed CTC system and show that the small perturbations affect only the center of mass motion and the global phase of the N-soliton train. A special reduction of CTC known as the Toda chain with indefinite metric describes the interaction of the sine-Gordon solitons and anti-solitons. The peculiarities of the interactions in the non-adiabatic cases are outlined.

nlin.SI↗

arXiv1997

Criterion and Regions of Stability for Quasi-Equidistant Soliton Trains

Using the complex Toda chain (CTC) as a model for the propagation of the N-soliton pulse trains of the nonlinear Schrodinger (NLS) equation, we predict the asymptotic behavior of these trains. The following asymptotic regimes are stable: (i)~asymptotically free propagation of all N solitons; (ii)~bound state regime where the N solitons may move quasi-equidistantly (QED); and (iii)~various different combinations of (i) and (ii). For N=2 and 3 we determine analytically the set of initial soliton parameters corresponding to each of these regimes. We find excellent agreement between the solutions of CTC and NLS for all regimes and propose realistic choices for the sets of amplitudes, for which the solitons propagate QED to very large run lengths. This is of importance for optical fiber communication.

solv-int↗