# Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials

## Abstract

A perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within an N-soliton train of the nonlinear Schroedinger equation. 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 a soliton train. An analytical expression for these critical strengths for expulsion is also derived.

- Authors:

- Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Blvd. Tzarigradsko chaussee 72, 1784 Sofia (Bulgaria)
- Dipartimento di Fisica 'E.R. Caianiello' and Consorzio Nazionale, Interuniversitario per le Scienze Fisiche della Materia (CNISM), Unita di Salerno, Universita di Salerno, via S. Allende, I84081 Baronissi (Saudi Arabia) (Italy)
- Institute for Electronics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko chaussee 72, 1784 Sofia (Bulgaria)

- Publication Date:

- OSTI Identifier:
- 20779248

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevE.73.046606; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; NONLINEAR PROBLEMS; PERIODICITY; PERTURBATION THEORY; POTENTIALS; SCHROEDINGER EQUATION; SOLITONS

### Citation Formats

```
Gerdjikov, V.S., Baizakov, B.B., Salerno, M., and Kostov, N.A.
```*Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVE.73.0.

```
Gerdjikov, V.S., Baizakov, B.B., Salerno, M., & Kostov, N.A.
```*Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials*. United States. doi:10.1103/PHYSREVE.73.0.

```
Gerdjikov, V.S., Baizakov, B.B., Salerno, M., and Kostov, N.A. Sat .
"Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials". United States.
doi:10.1103/PHYSREVE.73.0.
```

```
@article{osti_20779248,
```

title = {Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials},

author = {Gerdjikov, V.S. and Baizakov, B.B. and Salerno, M. and Kostov, N.A.},

abstractNote = {A perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within an N-soliton train of the nonlinear Schroedinger equation. 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 a soliton train. An analytical expression for these critical strengths for expulsion is also derived.},

doi = {10.1103/PHYSREVE.73.0},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 4,

volume = 73,

place = {United States},

year = {Sat Apr 15 00:00:00 EDT 2006},

month = {Sat Apr 15 00:00:00 EDT 2006}

}