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Communications in Theoretical Physics

Nonlinear Waves in a Cigar-Shaped Bose–Einstein Condensate with Dissipation

Yang Xiao-Xian, Yu-Ren Shi, Duan Wen-Shan

Published Jan 1, 2008• 8 citations
Publisher

Abstract

We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensate with dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t . The dissipative term of γ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.

DOI
10.1088/0253-6102/49/1/26

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We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensate with dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t . The dissipative term of γ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.
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.
We discuss the possible observation of a new type of standing nonlinear atomic matter wave in the condensate: the nonlinear impurity mode. It is investigated dynamical effects of a bright soliton in Bose-Einstein-condensed (BEC) systems with local space variations of the two-body atomic scattering length. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. Processes as trapping, reflection and transmission of the bright matter soliton due to the impurity are studied considering an analytical time-dependent variational approach and also by full numerical simulation. A condition is obtained for the collapse of the bright solitary wave in the quasi-one-dimensional BEC with attractive local inhomogeneity.