The existence of localized states in the Bose-Einstein condensate with two and three- body interactions in presence of nonlinearity management is shown. This result also obtained from Gross-Pitaevskii equation averaged over rapid modulations.
The evolution of matter-wave vector solitons in two dimensions under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation is derived. The averaging gives the appearance of the effective nonlinear quantum pressure depending on the population of the other component. Using this system of equations, the dynamical stabilization of the two-dimensional vector matter-wave solitons under the management of the mean-field nonlinearity is investigated. It is shown that the nonlinear quantum pressure arrests the collapse in the averaged system, giving rise to stable vector solitons. Full numerical simulations of the original, time-dependent system of Gross-Pitaevskii equations confirm that the management strongly prolongs the lifetime of these solitons compared to the unmanaged case.
We investigate the profiles and stability of the localized nonlinear matter waves in a Bose–Einstein condensate with spatially inhomogeneous two- and three-body interactions in various external potentials both analytically and numerically. Several families of localized stationary solutions of the one-dimensional mean-field Gross–Pitaevskii equation with cubic–quintic nonlinearities are obtained by similarity transformation. It is shown that the whole Bose–Einstein condensate can have an infinite number of localized nonlinear matter waves determined by certain non-negative integers. The linear and dynamical stabilities of the localized stationary solutions are studied numerically, and some stable localized nonlinear matter waves are found. We demonstrate that the attractive inhomogeneous two- and three-body interactions support linearly and dynamically stable localized nonlinear matter waves, but attractive two-body interaction along with repulsive three-body interaction destroys the linear stability. Moreover, an anharmonic potential is proposed to stabilize the localized nonlinear matter waves in the Bose–Einstein condensate with spatially inhomogeneous interactions.
Using the F-expansion method, we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized onedimensional Gross-Pitaevskii equation with time-dependent coefficients, for the experimentally relevant quadratic potential strength. Various shapes of the analytical matter-wave solutions which have important applications of physical interest are studied in detail. In particular, the matter-wave solitons are obtained in the quintic Gross-Pitaevskii equation model, which may be produced by tuning the cubic nonlinearity to zero via the Feschbach resonance technique. Direct numerical simulation has been performed to show the stable region of the matter-wave soliton.
By two direct assumption methods and symbolic computation, we present two families of one-soliton solutions and a family of two-soliton solutions with some arbitrary functions for the three-dimensional Gross—Pitaevskii equation with time-space modulation. Then we investigate the dynamics of these matter-wave solitons in three-dimensional Bose—Einstein condensates. We can see that the intensities of both one-solitons and two-solitons first increase rapidly to the condensation peak value, then decay very slowly to the background value. Thus these matter-wave solitons in three-dimensional Bose—Einstein condensates can remain for a sufficiently long time to be fully observed and modulated for real applications in today's experiments.
Abstract Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ ±1 are all stable, but the moving breathing soliton ψ 0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.
Using the F-expansion method we present analytical matter-wave solutions to Bose—Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross—Pitaevskii equation with time-dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain (loss). Various shapes of analytical matter-wave solutions which have important applications of physical interest are studied in details.