On the soliton interactions in NLS equation with external potentials

N. Kostov; V. Gerdjikov

doi:10.1117/12.727172

5 March 2007 On the soliton interactions in NLS equation with external potentials

N. Kostov, V. Gerdjikov

Proceedings Volume 6604, 14th International School on Quantum Electronics: Laser Physics and Applications; 66041S (2007) https://doi.org/10.1117/12.727172
Event: 14th International School on Quantum Electronics: Laser Physics and Applications, 2006, Sunny Beach, Bulgaria

Abstract

Perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions of N-soliton train of the nonlinear Schroedinger equation (NLS). Perturbations induced by weak quadratic and periodic external potentials are studied by both analytical and numerical means. It is found that 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 to a parabolic trap and optical lattice, as well as tilted periodic potentials. In the last case we demonstrate that there exist critical values of the strength of the linear potential for which one or more localized states can be extracted from the soliton train. An analytical expression for these critical strengths for expulsion is also derived.

Citation Download Citation

N. Kostov and V. Gerdjikov "On the soliton interactions in NLS equation with external potentials", Proc. SPIE 6604, 14th International School on Quantum Electronics: Laser Physics and Applications, 66041S (5 March 2007); https://doi.org/10.1117/12.727172

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