Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Scattering of a two-soliton molecule by Gaussian potential barriers and wells

Bakhram Umarov, Nor Amirah Busul Aklan, Bakhtiyor B. Baizakov, F. Kh. Abdullaev

Published Mar 1, 2016• 5 citations
Publisher

Abstract

Two anti-phase bright solitons in a dipolar Bose-Einstein condensate can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two- soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). At sufficiently low velocity of the incident molecule we observe quantum reflection from the potential well. Predictions of the mathematical model are compared with numerical simulations of the GPE, and good qualitative agreement between them is demonstrated.

DOI
10.1088/1742-6596/697/1/012023

Related papers

Scattering of a two-soliton molecule by attractive potential well

Bakhram Umarov, Bakhtiyor B. Baizakov, Nor Amirah Busul Aklan +1 more

Two anti-phase bright solitons in a dipolar Bose-Einstein condensate can form stable bound states, known as soliton molecules. In this paper we study the scattering of a twosoliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). At sufficiently low velocity of the incident molecule we observe quantum reflection from the potential well. Predictions of the mathematical model are compared with numerical simulations of the GPE, and good qualitative agreement between them is demonstrated.

•Jan 1, 2015•0 citations

Scattering of a two-soliton molecule by Gaussian potentials in dipolar Bose–Einstein condensates

Bakhram Umarov, Nor Amirah Busul Aklan, Bakhtiyor B. Baizakov +1 more

Abstract Two bright solitons in a dipolar Bose–Einstein condensate (BEC) can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two-soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Collisions of soliton molecules with single solitons are investigated, the latter playing the role of a localized defect. Due to the long-range character of dipolar forces solitons interact with each other even though their waveforms do not appreciably overlap. This is an essentially different feature of dipolar solitons compared to their counterparts in BECs with contact atomic interactions. The result of scattering significantly depends on the potential’s strength and velocity of collision. For weak potentials and/or low velocity the molecule preserves its coherence, meantime the internal modes are excited. Scattering by strong potentials at moderately high velocity ends up with dissociation of the molecule. The theoretical model is based on the variational approximation for the nonlocal Gross–Pitaevskii equation (GPE). Predictions of the mathematical model are compared with numerical simulations of the nonlocal GPE, and good qualitative agreement between them is demonstrated.

Journal of Physics B Atomic Molecular and Optical Physics•May 25, 2016•15 citations

Two-soliton molecule bouncing in a dipolar Bose–Einstein condensates under the effect of gravity

Kh. P. Khamrakulov

The dynamics of a two-soliton molecule bouncing on the reflecting atomic mirror under the effect of gravity have been studied by analytical and numerical methods. The analytical description is based on the variational approximation. In numerical simulations, we observe the resonance oscillations of the two-soliton’s center-of-mass position and width, induced by modulated atomic mirror. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation (GPE) and qualitative agreement between them is found. Hamiltonian dynamic system for a dipolar Bose–Einstein condensates (BECs) has been studied.

arXiv:1912.09398•Modern Physics Letters B•Nov 28, 2019•2 citations

Weakly bound solitons and two-soliton molecules in dipolar Bose–Einstein condensates

B B Baizakov, S. M. Al-Marzoug, Usama Al Khawaja +1 more

Abstract Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross–Pitaevskii equation and good qualitative agreement between them is demonstrated.

arXiv:1812.09563•Journal of Physics B Atomic Molecular and Optical Physics•Mar 8, 2019•8 citations

Interaction of solitons in one-dimensional dipolar Bose-Einstein condensates and formation of soliton molecules

Bakhtiyor B. Baizakov, S. M. Al-Marzoug, H. Bahlouli

The interaction between two bright solitons in a one-dimensional dipolar Bose-Einstein condensate (BEC) is investigated, with the aim of finding the regimes where they form a stable bound state, known as the soliton molecule. To study soliton interactions in BECs we employed a method similar to that used in experimental investigation of the interaction between solitons in optical fibers. The idea consists in creating two solitons at some spatial separation from each other at initial time ${t}_{0}$ and then measuring the distance between them at a later time ${t}_{1}>{t}_{0}$. Depending on whether the distance between solitons has increased, decreased, or remained unchanged, compared to its initial value at ${t}_{0}$, we conclude that the soliton interaction was repulsive, attractive, or neutral, respectively. We propose an experimentally viable method for estimating the binding energy of a soliton molecule, based on its dissociation at critical soliton velocity. Our theoretical analysis is based on the variational approach, which appears to be quite accurate in describing the properties of soliton molecules in dipolar BECs, as reflected in the good agreement between the analytical and the numerical results.

arXiv:1506.00923•Physical Review A•Sep 8, 2015•42 citations

Equilibrium and scattering properties of a nonlocal three-soliton molecule in Bose–Einstein condensates with competing nonlinearities

Khelifa Mohammed Elhadj, Abdelâali Boudjemâa

Abstract We carry out numerical and variational investigation of equilibrium and scattering properties of a bright three-soliton molecule in Bose–Einstein condensates with competing local and nonlocal nonlinearities in one-dimensional geometry. Our model predicts that the degree of the nonlocality and the soliton phase may strongly affect the binding energy and the soliton width. We show that the interaction of three solitons depends on their separation distance and on their relative phase. The scattering properties of these composite nonlinear structures by Gaussian potential barrier are analyzed variationally and numerically. It is found that stable transmission and reflection where the molecular structure is preserved can occur only for a specific barrier height and soliton velocity.

Physica Scripta•Nov 26, 2020•0 citations
Two anti-phase bright solitons in a dipolar Bose-Einstein condensate can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two- soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). At sufficiently low velocity of the incident molecule we observe quantum reflection from the potential well. Predictions of the mathematical model are compared with numerical simulations of the GPE, and good qualitative agreement between them is demonstrated.
Two anti-phase bright solitons in a dipolar Bose-Einstein condensate can form stable bound states, known as soliton molecules. In this paper we study the scattering of a twosoliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). At sufficiently low velocity of the incident molecule we observe quantum reflection from the potential well. Predictions of the mathematical model are compared with numerical simulations of the GPE, and good qualitative agreement between them is demonstrated.
Abstract Two bright solitons in a dipolar Bose–Einstein condensate (BEC) can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two-soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Collisions of soliton molecules with single solitons are investigated, the latter playing the role of a localized defect. Due to the long-range character of dipolar forces solitons interact with each other even though their waveforms do not appreciably overlap. This is an essentially different feature of dipolar solitons compared to their counterparts in BECs with contact atomic interactions. The result of scattering significantly depends on the potential’s strength and velocity of collision. For weak potentials and/or low velocity the molecule preserves its coherence, meantime the internal modes are excited. Scattering by strong potentials at moderately high velocity ends up with dissociation of the molecule. The theoretical model is based on the variational approximation for the nonlocal Gross–Pitaevskii equation (GPE). Predictions of the mathematical model are compared with numerical simulations of the nonlocal GPE, and good qualitative agreement between them is demonstrated.
The dynamics of a two-soliton molecule bouncing on the reflecting atomic mirror under the effect of gravity have been studied by analytical and numerical methods. The analytical description is based on the variational approximation. In numerical simulations, we observe the resonance oscillations of the two-soliton’s center-of-mass position and width, induced by modulated atomic mirror. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation (GPE) and qualitative agreement between them is found. Hamiltonian dynamic system for a dipolar Bose–Einstein condensates (BECs) has been studied.
Abstract Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross–Pitaevskii equation and good qualitative agreement between them is demonstrated.
The interaction between two bright solitons in a one-dimensional dipolar Bose-Einstein condensate (BEC) is investigated, with the aim of finding the regimes where they form a stable bound state, known as the soliton molecule. To study soliton interactions in BECs we employed a method similar to that used in experimental investigation of the interaction between solitons in optical fibers. The idea consists in creating two solitons at some spatial separation from each other at initial time t0{t}_{0}t0​ and then measuring the distance between them at a later time t1>t0{t}_{1}>{t}_{0}t1​>t0​. Depending on whether the distance between solitons has increased, decreased, or remained unchanged, compared to its initial value at t0{t}_{0}t0​, we conclude that the soliton interaction was repulsive, attractive, or neutral, respectively. We propose an experimentally viable method for estimating the binding energy of a soliton molecule, based on its dissociation at critical soliton velocity. Our theoretical analysis is based on the variational approach, which appears to be quite accurate in describing the properties of soliton molecules in dipolar BECs, as reflected in the good agreement between the analytical and the numerical results.
Abstract We carry out numerical and variational investigation of equilibrium and scattering properties of a bright three-soliton molecule in Bose–Einstein condensates with competing local and nonlocal nonlinearities in one-dimensional geometry. Our model predicts that the degree of the nonlocality and the soliton phase may strongly affect the binding energy and the soliton width. We show that the interaction of three solitons depends on their separation distance and on their relative phase. The scattering properties of these composite nonlinear structures by Gaussian potential barrier are analyzed variationally and numerically. It is found that stable transmission and reflection where the molecular structure is preserved can occur only for a specific barrier height and soliton velocity.