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

arXiv:cond-mat/0301319

On creation and evolution of dark solitons in Bose-Einstein condensates

Valeriy A. Brazhnyi, A. M. Kamchatnov, V. V. Konotop

Published Jan 17, 2003• 2 citations
arXivHTMLPDF

Abstract

Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton main characteristics of its motion such as a frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well. It is shown that long-time dynamics of a dark soliton in a generic situation deviates substantially from outcomes of the naive application of the Ehrenfest theorem. We also consider three different techniques of controllable creation of multi-soliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multi-soliton effects are discussed.

DOI
10.48550/arxiv.cond-mat/0301319

Related papers

Creation and evolution of trains of dark solitons in a trapped one-dimensional Bose-Einstein condensate

Valeriy A. Brazhnyi, A. M. Kamchatnov

The generation of dark solitons from large initial excitations and their evolution in a one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. We consider three different techniques of controllable creation of multisoliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multisoliton effects are discussed.

Physical Review A•Oct 13, 2003•31 citations

GENERATION AND EVOLUTION OF DARK-SOLITON TRAINS IN ONE-DIMENSIONAL BOSE–EINSTEIN CONDENSATES

QIANG TIAN, JINGPING WANG

Generation and evolution of dark-soliton trains are studied. We focus on the dynamics resulting from large initial excitations in one-dimensional Bose–Einstein condensates trapped by a harmonic potential numerically. We consider three different techniques of controllable creation of multisolition structures (soliton trains). Multisoliton effects are discussed.

International Journal of Modern Physics B•Mar 20, 2006•0 citations

Evolution of a dark soliton in a parabolic potential: Application to Bose-Einstein condensates

Valeriy A. Brazhnyi, V. V. Konotop

Evolution of a dark soliton in a one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a deep soliton, main characteristics of its motion such as frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well.

Physical Review A•Oct 13, 2003•55 citations

On-demand generation of dark soliton trains in Bose-Einstein condensates

A. Romero-Ros, G. C. Katsimiga, P. G. Kevrekidis +3 more

Matter-wave interference mechanisms in one-dimensional Bose-Einstein condensates that allow for the controlled generation of dark soliton trains upon choosing suitable box-type initial configurations are described. First, the direct scattering problem for the defocusing nonlinear Schr\"odinger equation with nonzero boundary conditions and general box-type initial configurations is discussed, and expressions for the discrete spectrum corresponding to the dark soliton excitations generated by the dynamics are obtained. It is found that the size of the initial box directly affects the number, size and velocity of the solitons, while the initial phase determines the parity of the solutions. The analytical results obtained for the untrapped system are compared to those of numerical simulations of the Gross-Pitaevskii equation, both in the absence and in the presence of a harmonic trap. The numerical results bear out the analytical results with excellent agreement.

arXiv:2009.02292•Physical Review A•Feb 24, 2021•23 citations

On-demand generation of dark-bright soliton trains in Bose-Einstein condensates

A. Romero-Ros, G. C. Katsimiga, P. G. Kevrekidis +3 more

The controlled creation of dark-bright (DB) soliton trains in multicomponent Bose-Einstein condensates (BECs) is a topic of ongoing interest. In this work we generalize earlier findings on the creation of dark soliton trains in single-component BECs [A. Romero-Ros et al., Phys. Rev. A 103, 023329 (2021)] to two-component BECs. By choosing suitable filled box-type initial configurations (FBTCs) and solving the direct scattering problem for the defocusing vector nonlinear Schr\"odinger equation with nonzero boundary conditions we obtain analytical expressions for the DB soliton solutions produced by a general FBTC. It is found that the size of the initial box and the amount of filling directly affect the number, size, and velocity of the solitons, while the initial phase determines the parity (even or odd) of the solutions. Our analytical results are compared to direct numerical integration of the coupled Gross-Pitaevskii equations, both in the absence and in the presence of a harmonic trap, and an excellent agreement between the two is demonstrated.

arXiv:2109.11351•Physical Review A•Feb 24, 2022•7 citations

Dark solitons as quasiparticles in trapped condensates

Valeriy A. Brazhnyi, V. V. Konotop, Лев П. Питаевский

We present a theory of dark soliton dynamics in trapped quasi-one-dimensional Bose-Einstein condensates, which is based on the local-density approximation. The approach is applicable for arbitrary polynomial nonlinearities of the mean-field equation governing the system as well as to arbitrary polynomial traps. In particular, we derive a general formula for the frequency of the soliton oscillations in confining potentials. A special attention is dedicated to the study of the soliton dynamics in adiabatically varying traps. It is shown that the dependence of the amplitude of oscillations vs the trap frequency (strength) is given by the scaling law ${X}_{0}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}\ensuremath{\gamma}}$ where the exponent $\ensuremath{\gamma}$ depends on the type of the two-body interactions, on the exponent of the polynomial confining potential, on the density of the condensate, and on the initial soliton velocity. Analytical results obtained within the framework of the local-density approximation are compared with the direct numerical simulations of the dynamics, showing a remarkable match. Various limiting cases are addressed. In particular for the slow solitons we computed a general formula for the effective mass and for the frequency of oscillations.

arXiv:cond-mat/0603197•Physical Review A•May 3, 2006•55 citations
Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton main characteristics of its motion such as a frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well. It is shown that long-time dynamics of a dark soliton in a generic situation deviates substantially from outcomes of the naive application of the Ehrenfest theorem. We also consider three different techniques of controllable creation of multi-soliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multi-soliton effects are discussed.
The generation of dark solitons from large initial excitations and their evolution in a one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. We consider three different techniques of controllable creation of multisoliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multisoliton effects are discussed.
Matter-wave interference mechanisms in one-dimensional Bose-Einstein condensates that allow for the controlled generation of dark soliton trains upon choosing suitable box-type initial configurations are described. First, the direct scattering problem for the defocusing nonlinear Schr\"odinger equation with nonzero boundary conditions and general box-type initial configurations is discussed, and expressions for the discrete spectrum corresponding to the dark soliton excitations generated by the dynamics are obtained. It is found that the size of the initial box directly affects the number, size and velocity of the solitons, while the initial phase determines the parity of the solutions. The analytical results obtained for the untrapped system are compared to those of numerical simulations of the Gross-Pitaevskii equation, both in the absence and in the presence of a harmonic trap. The numerical results bear out the analytical results with excellent agreement.
The controlled creation of dark-bright (DB) soliton trains in multicomponent Bose-Einstein condensates (BECs) is a topic of ongoing interest. In this work we generalize earlier findings on the creation of dark soliton trains in single-component BECs [A. Romero-Ros et al., Phys. Rev. A 103, 023329 (2021)] to two-component BECs. By choosing suitable filled box-type initial configurations (FBTCs) and solving the direct scattering problem for the defocusing vector nonlinear Schr\"odinger equation with nonzero boundary conditions we obtain analytical expressions for the DB soliton solutions produced by a general FBTC. It is found that the size of the initial box and the amount of filling directly affect the number, size, and velocity of the solitons, while the initial phase determines the parity (even or odd) of the solutions. Our analytical results are compared to direct numerical integration of the coupled Gross-Pitaevskii equations, both in the absence and in the presence of a harmonic trap, and an excellent agreement between the two is demonstrated.
We present a theory of dark soliton dynamics in trapped quasi-one-dimensional Bose-Einstein condensates, which is based on the local-density approximation. The approach is applicable for arbitrary polynomial nonlinearities of the mean-field equation governing the system as well as to arbitrary polynomial traps. In particular, we derive a general formula for the frequency of the soliton oscillations in confining potentials. A special attention is dedicated to the study of the soliton dynamics in adiabatically varying traps. It is shown that the dependence of the amplitude of oscillations vs the trap frequency (strength) is given by the scaling law ${X}_{0}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}\ensuremath{\gamma}}$ where the exponent $\ensuremath{\gamma}$ depends on the type of the two-body interactions, on the exponent of the polynomial confining potential, on the density of the condensate, and on the initial soliton velocity. Analytical results obtained within the framework of the local-density approximation are compared with the direct numerical simulations of the dynamics, showing a remarkable match. Various limiting cases are addressed. In particular for the slow solitons we computed a general formula for the effective mass and for the frequency of oscillations.