Controlling the collision between two solitons in the condensates by a double-barrier potential

We present an analytical solution of two solitons of Bose-Einstein condensates trapped in a double-barrier potential by using a multiple-scale method. In the linear case, we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence. For weak nonlinearity, it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties. Especially, in the case of regarding a double-barrier potential as the output source of the solitons, the collision spots between two dark solitons can be controlled by the height of the barrier potential.

Dynamics of vector solitons in two-component Bose-Einstein condensates with time-dependent interactions and harmonic potential

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schrodinger equations with time- varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright sol/tons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our modeh At the same time, we obtain the opposite situation for dark-dark solitons.

Interactions between bright solitons in different species of Bose-Einstein condensates

The dynamics of a bright bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied. The interaction between bright solitons in different species with small separation is derived. Unlike the interaction between solitons of the same species, it is independent of the phase difference between solitons. It may be of attraction or repulsion. In the former case, each soliton will oscillate about and pass through each other around the mass-center of the system, which will also oscillate harmonically due to the harmonic trapping potential.

Matter-Wave Solitons in Two-Component Bose—Einstein Condensates with Tunable Interactions and Time Varying Potential

We present three families of exact matter-wave soliton solutions for an effective one-dimension twocomponent Bose-Einstein condensates(BECs) with tunable interactions,harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons,bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential,periodically modulated harmonic trap potential,and kinklike modulated harmonic trap potential.Through the Feshbach resonance,these dynamics can be realized in experiments by suitable control of time-dependent trap parameters,atomic interactions,and interaction with thermal cloud.

Stabilised bright solitons in Bose-Einstein condensates in an expulsive parabolic and complex potential

The exact solitonic solutions of the one-dimensional nonlinear Schroedinger equation, which describes the dynamics of bright soliton in Bose-Einstein condensates with the time-dependent interaction in an expulsive parabolic and complex potential, are obtained by Darboux transformation. The results show that one can compress a bright soliton into an assumed peak of matter wave density by adusting the experimental parameter of the ratio of axial oscillation to radial oscillation or feeding parameter. Especially, when parameters satisfy the relation λ = 2γ the soliton is stable with time evolution without changing its shape and amplitude.

Dynamic stability and manipulation of bright matter-wave solitons by optical lattices in Bose-Einstein condensates

An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a timespace periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.

Feshbach resonance management of vector solitons in two-component Bose-Einstein condensates

We consider two coupled Gross Pitaevskii equations describing a two-component Bose Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential, and investigate the dynamics of vector solitons. By using a direct method, we construct a novel family of vector soliton solutions, which are the linear combination between dark and bright solitons in each component. Our results show that due to the superposition between dark and bright solitons, such vector solitons possess many novel and interesting properties. The dynamics of vector solitons can be controlled by the Feshbach resonance technique, and the vector solitons can keep the dynamic stability against the variation of the scattering length.

Effects of periodic optical lattice potential on dark solitons in a Bose Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose-Einstein condensate with a magnetic trap and an optical lattice （OL） trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.

Soliton dynamical properties of Bose Einstein condensates trapped in a double square well potential

We first present an analytical solution of the single and double solitions of Bose-Einstein condensates trapped in a double square well potential using the multiple-scale method. Then, we show by numerical calculation that a dark soliton can be transmitted through the square well potential. With increasing depth of the square well potential, the amplitude of the dark soliton becomes larger, and the soliton propagates faster. In particular, we treat the collision behaviour of the condensates trapped in either equal or different depths of the double square well potential. If we regard the double square well potential as the output source of the solitons, the collision locations （position and time） between two dark solitons can be controlled by its depth.

Head-on collision of ring dark solitons in Bose-Einstein condensates

The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.

Formation of combined solitons in two-component Bose—Einstein condensates

We investigate the combined soliton solutions of two-component Bose-Einstein condensates with external potential. The ＂phase diagram＂ is obtained for the formation regions of different combined solitons. Our results show that the intraspecies （interspecies） interaction strengths and the external trapped potential clearly affect the formation of dark- dark, bright-bright, and dark bright soliton solutions in different regions. Especially, we find that the bright bright （dark^dark） soliton can exist in the case of both repulsive （attractive） intraspecies interaction strengths in the presence of external potential. This novel phenomenon is completely different from the formation of soliton solution of one- component Bose-Einstein condensates without external potential, and it will be useful for the study of two-component Bose-Einstein condensates.

Effect of interaction strength on gap solitons of Bose-Einstein condensates in optical lattices

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose-Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose-Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose-Einstein condensate.

Matter-Wave Solitons in Two-Dimensional Bose—Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Trap

We present three families of one-soliton solutions for (2+l)-dimensional Gross-Pitaevskii equation withboth time-dependent scattering length and gain or loss in a harmonic trap.Then we investigate the dynamics of thesesolitons in Bose-Einstein condensates (BECs) by some selected control functions.Our results show that the intensitiesof these solitons first increase rapidly to the condensation peak,then decay very slowly to the background;thus thelifetime of a bright soliton,a train of bright solitons and a dark soliton in BECs can be all greatly extended.Our resultsoffer a useful method for observing matter-wave solitons in BECs in future experiments.

Stability properties of vector solitons in two-component Bose-Einstein condensates with tunable interactions

By using a unified theory of the formation of various types of vector-solitons in two-component Bose-Einstein condensates with tunable interactions, we obtain a family of exact vector-soliton solutions for the coupled nonlinear Schrodinger equations. Moreover, the Bogoliubov equation shows that there exists stable dark soliton in specific situa- tions. Our results open up new ways in considerable experimental interest for the quantum control of multi-component Bose Einstein condensates.

Three-dimensional solitons in two-component Bose–Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.

Three-dimensional Bose Einstein condensate vortex solitons under optical lattice and harmonic confinements

We predict three-dimensional vortex solitons in a Bose-Einstein condensate under a complex potential,which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction.The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction.This has not been reported before in the three-dimensional Bose-Einstein condensate.By using a combination of the energy density functional method with direct numerical simulation,we find three-dimensional vortex solitons with topological charges χ=1,χ=2,and χ=3.Moreover,the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution.Therein,the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling.Specifically,we successfully manipulate the vortex solitons along the optical lattice direction.The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.

Nonautonomous deformed solitons in a Bose-Einstein condensate

We study exact single-soliton solutions of an attractive Bose-Einstein condensate governed by a one-dimensional nonautonomous Gross-Pitaevskii system. For several different forms of time-dependent atom-atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton＇s center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions.

Controlling the motion of solitons in BEC by a weakly periodic potential

By developing multiple-scale method combined with Wentzel-Kramer-Brillouin expansion, this paper analytically studies the modulating effect of weakly periodic potential on the dynamical properties of the Dose-Einstein condensates （BEC） trapped in harmonic magnetic traps. A black-grey soliton transition is observed in the BEC trapped in harmonic magnetic potential, due to the weakly periodic potential modulating effect. Meanwhile, it finds that with the slight increase of the weakly periodic potential strength, the velocity of the soliton decreases, while its width firstly decreases then increases, a minimum exists there. These results show that the amplitude, velocity, and width of matter solitons can be effectively managed by means of a weakly periodic potential

Controlling the Collision Between Two Solitons in a Two-Component Condensate by Interspecies Interactions

We present a family of the solutions of two-component Bose-Einstein condensates with time-dependentscattering length by means of multiple-scale method.Our numerical calculations show that the collision properties (theposition,the time,and the frequency of the collision) between two solitons can be controlled by the time-dependentinterspecies scattering length.Meanwhile,we also find that the amplitude of the solitons is close related to the timedependentinterspecies scattering length.

Nonautonomous dark soliton solutions in two-component Bose–Einstein condensates with a linear time-dependent potential

We report the analytical nonantonomous soliton solutions （NSSs） for two-component Bose-Einstein condensates with the presence of a time-dependent potential. These solutions show that the time-dependent potential can affect the velocity of NSS. The velocity shows the characteristic of both increasing and oscillation with time. A detailed analysis for the asymptotic behavior of NSSs demonstrates that the collision of two NSSs of each component is elastic.