Asymptotic Behavior ofN-Soliton Trains of the Nonlinear Schrödinger Equation

Interaction ofNsolitons in the massive Thirring model and optical gap system: The complex Toda chain model

“…In Refs. [3,4,7] and [10] the comparison of the complex Toda chain predictions with the numerical solutions of the NLS and MNLS equations has been performed and a good agreement has been established for various choices of the initial parameters of the solitons in the train.…”

“…The complex Toda chain allows a rich class of asymptotic regimes of the soliton train propagation [3,6,7]: i ) asymptotically free propagation of solitons, ii ) N-soliton bound states with the possibility of a quasi-equidistant propagation, iii ) mixed asymptotic regimes when part of the solitons form bound state(s) and the rest separate from them, iv ) regimes corresponding to the degenerate and singular solutions of the complex Toda chain. The rich variety of dynamical regimes of the complex Toda chain indicates that it is a good candidate for analytical study of the soliton trains.…”

“…Recently the complex Toda chain attracted much attention as a possible candidate for description of the pulse interactions in integrable and non-integrable nonlinear evolution equations [1,2,3,4,5,6,7,8,9,10]. For instance, it was shown that the complex Toda chain describes the soliton train propagation for all the nonlinear evolution equations associated with the NLS hierarchy [9].…”

Modeling Adiabatic N-Soliton Interactions and Perturbations

“…[2,3,4,5,12,16]. Recently with the realization of Bose-Einstein condensation of dilute atomic gases it became important to study NLS equation with additional potential term iR[u] = V (x)u(x, t), see [17,18].…”

“…started with the pioneering paper [1], by now has been extensively studied (see [2,3,4,5,6] and references therein). Several other nonlinear evolution equations (NLEE) were also studied, among them the modified NLS equation [8,9,10,11,12], some higher NLS equations [6], the Ablowitz-Ladik system [7] and others.…”