On modelling adiabatic N - soliton interactions in external potentials

Abstract

We analyze perturbed version of the complex Toda chain (CTC) in an attempt to describe the adiabatic N - soliton train interactions of the perturbed nonlinear Schrödinger equation (NLS). We study perturbations with weak quadratic and periodic external potentials by both analytical and numerical means. The perturbed CTC adequately models the N - soliton train dynamics for both types of potentials. As an application of the developed theory we consider the dynamics of a train of matter - wave solitons confined in a parabolic trap and optical lattice, as well as tilted periodic potential.

14 pages, 7 figures; added subsection and references

References in corpus (5)

• Formation and Propagation of Matter Wave Soliton Trains
• Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential
• Localized breathing solutions for Bose-Einstein condensates in periodic traps
• Perturbation theory for the modified nonlinear Schr{ö}dinger solitons
• Adiabatic Interaction of N Ultrashort Solitons: Universality of the Complex Toda Chain Model

Cited by in corpus (2)

• Supersolitons: Solitonic excitations in atomic soliton chains
• Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials