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 Henan University

The Nonlinear Properties of Solitary Wave in Two Dimensional-Bose-Einstein Condensation

Yonglian Chen

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

The solition wave in Bose-Einstein condensate with disk-shaped trap is investigated in this paper.Under the mean feld,a two-dimensional nonlinear Schrdinger equation is obtained.By using the transverse perturbation method,a(KdV)equation for the nonlinear electron acoustic solitary waves is derived.The soliton solution is also obtained.It is found that the coupling parameter of interaction between scattering length and Bose depends on solitary waves.

Related papers

KdV Description in Fermi-Einstein Condensates

Suo Nan-ji

It was studied that superfluid Fermi gas in a two-dimensional solitary wave pulses in the mean-field theory for superfluid gas under limiting conditions unitarity regional and BEC regions in this paper. By using the transverse perturbation method,a( Kd V) equation for the nonlinear electron acoustic solitary waves was derived.It was found that the amplitude,width and scattering length of the solitary waves were depended on the parameters.

Jilin Normal University Journal•Jan 1, 2016•0 citations

The modulational instability of the solition wave in two-dimensional Bose-Einstein condensates

Heng Zhang, Duan Wen-Shan

The solition wave in Bose-Einstein condensate with disk-shaped trap is investigated in this paper. Beyond the mean field, a two-dimensional nonlinear Schrödinger equation is obtained. The modulational instability for this system is studied analytically, and the growth rate for it is given.

Acta Physica Sinica•Jan 1, 2013•3 citations

Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap

Guoxiang Huang, Valeri A. Makarov, Manuel G. Velárde

We consider, both analytically and numerically, the evolution of two-dimensional (2D) nonlinear matter-wave pulses in a Bose-Einstein condensate with a disk-shaped trap and repulsive atom-atom interactions. Due to the strong confinement in the axial direction the sound speed of the system is ${c=(1/2}^{1/4}{)c}_{0},$ where ${c}_{0}$ is the corresponding value without the trap. From the 3D order-parameter equation of the condensate, we derive a soliton-bearing Kadomtsev-Petriashvili equation with positive dispersion. When the trapping potential is weak in two transverse directions, a low-depth plane dark soliton can propagate in the condensate with a changing profile but preserving its structure down to the boundary of the condensate. We show that high-depth plane dark solitons are unstable to long-wavelength transverse disturbances. The instability appears as a longitudinal modulation of the soliton amplitude decaying into vortices. We also show how a dark lumplike 2D nonlinear excitation can be excited in the system. Furthermore, a dark lump decaying algebraically in two spatial directions can propagate rather stable in the condensate, but disappears near the boundary of the condensate where two vortices are nucleated. The vortices move in opposite directions along the boundary and when meeting merge creating a new lump. Finally, we also provide results for head-on and oblique collisions of two lumps in the system.

Physical Review A•Feb 13, 2003•119 citations

Weak nonlinear matter waves in a trapped two-component Bose–Einstein condensates

Yong Wen-Mei, Ju-Kui Xue

The dynamics of the weak nonlinear matter solitary waves in two-component Bose–Einstein condensates (BEC) with cigar-shaped external potential are investigated analytically by a perturbation method. In the small amplitude limit, the two-components can be decoupled and the dynamics of solitary waves are governed by a variable-coefficient Korteweg–de Vries (KdV) equation. The reduction to the KdV equation may be useful to understand the dynamics of nonlinear matter waves in two-component BEC. The analytical expressions for the evolution of soliton, emitted radiation profiles and soliton oscillation frequency are also obtained.

Physica Scripta•Feb 6, 2008•3 citations

Dynamics of bright matter-wave solitons in a Bose–Einstein condensate with inhomogeneous scattering length

F. Kh. Abdullaev, A. Gammal, Lauro Tomio

We investigate dynamical effects of a bright soliton in Bose–Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross–Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 23, 2004•37 citations

Two-Dimensional Soliton Interaction for Multi-component Bose–Einstein Condensates

Sheng-Chang Li, Duan Wen-Shan

For two-component disk-shaped Bose–Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev–Petviashvili-I equation at the lowest order from the original coupled Gross–Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev–Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.

Communications in Theoretical Physics•Sep 1, 2008•3 citations
The solition wave in Bose-Einstein condensate with disk-shaped trap is investigated in this paper.Under the mean feld,a two-dimensional nonlinear Schrdinger equation is obtained.By using the transverse perturbation method,a(KdV)equation for the nonlinear electron acoustic solitary waves is derived.The soliton solution is also obtained.It is found that the coupling parameter of interaction between scattering length and Bose depends on solitary waves.
We consider, both analytically and numerically, the evolution of two-dimensional (2D) nonlinear matter-wave pulses in a Bose-Einstein condensate with a disk-shaped trap and repulsive atom-atom interactions. Due to the strong confinement in the axial direction the sound speed of the system is c=(1/21/4)c0,{c=(1/2}^{1/4}{)c}_{0},c=(1/21/4)c0​, where c0{c}_{0}c0​ is the corresponding value without the trap. From the 3D order-parameter equation of the condensate, we derive a soliton-bearing Kadomtsev-Petriashvili equation with positive dispersion. When the trapping potential is weak in two transverse directions, a low-depth plane dark soliton can propagate in the condensate with a changing profile but preserving its structure down to the boundary of the condensate. We show that high-depth plane dark solitons are unstable to long-wavelength transverse disturbances. The instability appears as a longitudinal modulation of the soliton amplitude decaying into vortices. We also show how a dark lumplike 2D nonlinear excitation can be excited in the system. Furthermore, a dark lump decaying algebraically in two spatial directions can propagate rather stable in the condensate, but disappears near the boundary of the condensate where two vortices are nucleated. The vortices move in opposite directions along the boundary and when meeting merge creating a new lump. Finally, we also provide results for head-on and oblique collisions of two lumps in the system.
The dynamics of the weak nonlinear matter solitary waves in two-component Bose–Einstein condensates (BEC) with cigar-shaped external potential are investigated analytically by a perturbation method. In the small amplitude limit, the two-components can be decoupled and the dynamics of solitary waves are governed by a variable-coefficient Korteweg–de Vries (KdV) equation. The reduction to the KdV equation may be useful to understand the dynamics of nonlinear matter waves in two-component BEC. The analytical expressions for the evolution of soliton, emitted radiation profiles and soliton oscillation frequency are also obtained.
We investigate dynamical effects of a bright soliton in Bose–Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross–Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.
For two-component disk-shaped Bose–Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev–Petviashvili-I equation at the lowest order from the original coupled Gross–Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev–Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.