Zong Feng-De

Optical Solitary Waves in Fourth-Order Dispersive Nonlinear Schrödinger Equation with Self-steepening and Self-frequency Shift

By making use of the generalized sine-Gordon equation expansion method, we find cnoidal periodic wave solutions and fundamental bright and dark optical solitary wave solutions for the fourth-order dispersive and the quintic nonlinear Schrodinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves.

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.

Adomian Decomposition Method for Nonlinear Differential-Difference Equation

Adomian decomposition method is applied to find the analytical and numerical solutions for the discretized mKdV equation. A numerical scheme is proposed to solve the long-time behavior of the discretized mKdV equation. The procedure presented here can be used to solve other differential-difference equations.

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 time-space 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.

Controlled Manipulation with a Bose–Einstein Condensates N-Soliton Train under the Influence of Harmonic and Tilted Periodic Potentials

A model of the perturbed complex Toda chain (PCTC) to describe the dynamics of a Bose–Einstein condensate (BEC) N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.

Vortical Solitons of Three-Dimensional Bose–Einstein Condensates under Both a Bichromatic Optical Lattice and Anharmonic Potentials

We study Bose—Einstein condensate vortical solitons under both a bichromatic optical lattice and anharmonic potential. The vortical solitons are built in the form of a layer-chain structure made up of two fundamental vortices along the bichromatic optical lattice direction, which have not been reported before in the three-dimensional Bose—Einstein condensate. A variation approach is applied to find the optimum initial solutions of vortical solitons. The stabilities of the vortical solitons are confirmed by the numerical simulation of the time-dependent Gross—Pitaevskii equation. In particular, stable Bose—Einstein condensate vortical solitons with fundamental vortices of different atomic numbers in the external potential within a range of experimentally achievable timescales are found. We further manipulate the vortical solitons to an arbitrary position by steadily moving the bichromatic optical lattice, and find a stable region for the successful manipulation of vortical solitons without collapse. These results provide insight into controlling and manipulating the Bose—Einstein condensate vortical solitons for macroscopic quantum applications.

Dynamics and Manipulation for Gap Solitons in Bose—Einstein Condensates under Optical Lattice and Harmonic Potentials

By means of an extended variational approach, we study dynamics for gap solitons in a repulsive interaction Bose—Einstein condensate under both a harmonic and an optical lattice confinement. The simplified analytic theory gives the critical strength ratio of harmonic to optical lattice necessary to support multiple stable lattice sites for the condensate. Moreover, we use numerical experiments to guide and manipulate the gap solitons to an arbitrary position via a time-dependent potential. All predictions of the extended variational approach are reasonably close to results of the simulations. In particular, the variational model helps capture the composition relationship between the variations of chirp and amplitude.