Elliptical Gaussian solitons in synthetic nonlocal nonliear media

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a "double-self-focusing" synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality.Based on the variational approach,it obtains the approximately analytical solution of such Gaussian elliptical solitons.It also computes the stability of the solitons by numerical simulations.     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.     

Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential

This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrdinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential.The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates.The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential.The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates.The collision of two dark solitons is nearly elastic.     

A novel type of solitons in electron-ion plasmas

By using one-dimensional self-consistent relativistic fluid model,a novel type of moving relativistic electro magnetic solitons with high intensity in electron-ion plasmas where the ion dynamics is taken into account is investigated numerically.Unlike solitons with single-humped scalar potential found in previous studies,these solitons possess multi-humped scalar and vector potential.The existence of such soliton solutions is investigated in plasmas with different background densities,and the properties of these solitons are presented in detail.We found that the peculiar profile of electron density has alternating regions of humps and dips like a Bragg's grating.     

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.     

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.     

A novel type of solitons in electron-ion plasmas

By using one-dimensional self-consistent relativistic fluid model, a novel type of moving relativistic electromagnetic solitons with high intensity in electron-ion plasmas where the ion dynamics is taken into account is investigated numerically. Unlike solitons with single-humped scalar potential found in previous studies, these solitons possess multi-humped scalar and vector potential. The existence of such soliton solutions is investigated in plasmas with different background densities, and the properties of these solitons are presented in detail. We found that the peculiar profile of electron density has alternating regions of humps and dips like a Bragg's grating.     

Effects of high-order dispersions on dark-bright vector soliton propagation and interaction

The dynamics of dark-bright vector solitons is investigated in a birefringent fiber with the high-order dispersions,and their effects on vector soliton propagation and interaction are analyzed using the numerical method.The combined role of the high-order dispersions,such as the third-order dispersion (TOD) and the fourth-order dispersion (FOD),may cause various deformation of the vector soliton and enhance interaction.These effects depend strictly on the sign of the high-order dispersions.Results indicate that the disadvantageous effects can be reduced effectively via proper mapping of the high-order dispersions.     

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.     

Effects of external magnetic trap on two dark solitons of a two-component Bose-Einstein condensate

Two dark solitons are considered in a two-component Bose-Einstein condensate with an external magnetic trap,and effects of the trap potential on their dynamics are investigated by the numerical simulation. The results show that the dark solitons attract,collide and repel periodically in two components as time changes,the time period depends strictly on the initial condition and the potential,and there are obvious self-trapping effects on the two dark solitons.     

Effect of Time-Dependent Atomic Scattering Length on Solitons in Bose-Einstein Condensates with a Complex Potential

We consider the one-dimensional nonlinear Schrǒdinger equations that describe the dynamics of a Bose-Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrǒdinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton.     

Dynamics of the Manakov Solitons in Biased Guest-Host Photorefractive Polymer

In the biased guest-host photorefractive polymer,the Manakov equations can be used to describe the optical soliton propagation and interaction.Hereby for such equations,via the Hirota method and symbolic computation,analytic soliton solutions in the bright-dark and dark-dark forms are obtained.Based on the choice of photorefractive polymer parameter and incident-optical-beam parameter,the bright-dark and dark-dark solitons as well as their interaction can occur in the polymer when the total intensity is much lower than the background illumination,and our analysis indicates that the incident light with different polarization directions influence little on the soliton propagation.γ,representing the soliton intensity far away from the soliton center,determines the appearance of bright or dark soliton under the background illumination.Through the graphic and asymptotic analysis on the two-soliton solutions along with the different γ,we find that there exist the elastic and inelastic interactions between the bright-dark solitons,while the interactions between the dark-dark solitons are always elastic.     

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.     

Dromion and Multi—soliton Structures of the （2＋1）—Dimensional Higher—Order Broer—Kaup System

Using the standard truncated Painleve analysis and the Backlund transformation,we can obtain many significant exact soliton solutions of the (2 1)-dimensional higher-order Broer-Kaup(HBK) system.A special type of soliton solution is described by the variable coefficient heat-conduction-liker equation.The inclusion of three arbitrary functions in the general expressions of the solitons makes the solitons of the (2 1)-dimensional HBK system possess abundant structures such as solitoff solutions,multi-dromion solutions,ring solitons and so on.     

Dark Solitons for the Defocusing Cubic Nonlinear Schr?dinger Equation with the Spatially Periodic Potential and Nonlinearity

We study the existence of dark solitons of the defocusing cubic nonlinear Schr¨odinger(NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincar′e map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.     

Two-Dimensional Spatial Solitons in Nematic Liquid Crystals

We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Oaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.     

Dark Soliton of a Growing Bose--Einstein Condensate in an External Trap

The dynamics of dark soliton in a growing Bose-Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.     

Nonlinear Wave in a Disc-Shaped Bose-Einstein Condensate

We discuss the possible nonlinear waves of atomic matter wave in a Bose-Einstein condensate. One and two of two-dimensional （2D） dark solitons in the Bose-Einstein condensed system are investigated. A rich dynamics is studied for the interactions between two solitons. The interaction profiles of two solitons are greatly different if the angle between them are different. If the angle is small enough, the maximum amplitude during the interaction between two solitons is even less than that of a single soliton. However, if the angle is large enough, the maximum amplitude of two solitons can gradually attend to the sum of two soliton amplitudes.     

Collision induced splitting of bright soliton in Bose--Einstein condensate

This paper studies the collision dynamics of bright soliton in Bose--Einstein condensate with trapezoid potential. It is found that besides the total reflection and total transmission, one bright soliton can be divided into two bright solitons with different amplitudes in a controllable manner.     

Asymmetrical surface soliton trains

We elucidate the existence, stability and propagation dynamics of multi-spot soliton packets in focusing saturable media. Such solitons are supported by an interface beside which two harmonically photonic lattices with different modulation depths are imprinted. We show that the surface model can support stable higher-order structures in the form of asymmetrical surface soliton trains, which is in sharp contrast to homogeneous media or uniform harmonic lattice modulations where stable asymmetrical multi-peaked solitons do not exist. Surface trains can be viewed as higher-order soliton states bound together by several different lowest order solitons with appropriate relative phases. Their existence as stable objects enriches the concept of compact manipulation of several different solitons as a single entity and offers additional freedom to control the shape of solitons by adjusting the modulation depths beside the interface.