Two types of ground-state bright solitons in a coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate

We study two types of bright solitons in an attractive Bose-Einstein condensate with a spin-orbit interaction. By solving the coupled nonlinear SchrOdinger equations with the variational method and the imaginary time evolution method, fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength. The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate.

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.

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose-Einstein condensate with a spin-orbit interaction. By solving the coupled nonlinear Scbrodinger equation with the variational method and the imaginary time evolution method, two kinds of solitons （plane wave soliton and stripe solitons） are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.

Merging and splitting dynamics between two bright solitons in dipolar Bose-Einstein condensates

We numerically study the interaction dynamics of two bright solitons with zero initial velocities in the one-dimensional dipolar Bose-Einstein condensates.Under different dipolar strengths,the two bright solitons can merge into a breathing wave,and then split or propagate constantly after several oscillating periods.We quantitatively study the breathing frequency of wave after merging and the asymmetry property of solitons after splitting,and analyze their formation mechanism by the system's energy evolution.Also,the change of initial phase difference brings distinct effects on the soliton interaction.Our results provide insight into the new dynamical phenomena in dipolar systems and enrich the understanding for interaction between dipolar solitons.

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.

Oscillation properties of matter–wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter-and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton(without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.

Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide

We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on Lax pair obtained by us,we derive the infinitely-many conservation laws.We give the bright one-,two-,and N-soliton solutions,and the first-,second-,and Nth-order breather solutions based on the N-fold DT.We conclude that the velocities of the bright solitons are influenced by the distributed gain function,g(z),and variable coefficients in equation,h1(z),p1(z),r1(z),and s1(z)via the asymptotic analysis,where z represents the propagation variable or spatial coordinate.We also graphically observe that:the velocities of the first-and second-order breathers will be affected by h1(z),p1(z),r1(z),and s1(z),and the background wave depends on g(z).

Bright Solitons on Continuous Wave Background in Blood Vessels

The nonlinear Schr6dinger equation （NLSE） with variable coefficients in blood vessels is discussed via an NLSE-based constructive method, and exact solutions are obtained including multi-soliton solutions with and without continuous wave backgrounds. The dynamical behaviors of these soliton solutions are studied. The solitonic propagation behaviors such as restraint and sustainment on continuous wave background are discussed by altering the value of dispersion parameter δ. Moreover, the longitude controllable behaviors are also reported by modulating the dispersion parameter ＆ These results are potential1y useful for future experiments in various blood vessels.

Experimental Observation of Bright and Dark Solitons Mode-Locked with Zirconia-Based Erbium-Doped Fiber Laser

We demonstrate the generation of dark and bright solitons with our homemade zirconia-based erbium-doped fiber and graphene oxide（GO） saturable absorber in anomalous dispersion region.The GO is fabricated using an abridged Hummer＇s method,which is combined with polyethylene oxide to produce a composite film.The film is sandwiched between two optical ferrules and embedded in the laser cavity to enhance its birefringence and nonlinearity.The self-starting bright soliton is easily generated at pump power of 78 mW with the whole length cavity of 14.7 m.The laser produces the bright pulse train with repetition rate,pulse width,pulse energy and central wavelength being 13.9 MHz,0.6 ps,2.74 p J and 1577.46 nm,respectively.Then,by adding the 10 m of single mode fiber into the laser cavity,dark soliton pulse is produced.For the formation of dark pulse train,the measured repetition rate,pulse width,pulse energy and central wavelength are 8.3 MHz,20 ns and 4.98 p J and1596.82 nm,respectively.Both pulses operate in the anomalous region.

Solitons and Bifurcations for the Generalized Tzitzéica Type Equation in Nonlinear Fiber Optics

Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation theory of differential equations, the bifurcation parameter conditions and all the bifurcation phase portraits are obtained. Because the same energy value of the Hamiltonian function is corresponding to the same orbit, thus the periodic wave solutions, bright soliton and dark soliton solutions are defined.

Optical Rogue Wave Excitation and Modulation on a Bright Soliton Background

We study rogue waves in an inhomogeneous nonlinear optical fiber with variable coefficients. An exact rogue wave solution that describes rogue wave excitation and modulation on a bright soliton pulse is obtained. Special properties of rogue waves on the bright soliton, such as the trajectory and spectrum, are analyzed in detail. In particular, our analytical results suggest a way of sustaining the peak shape of rogue waves on the soliton background by choosing an appropriate dispersion parameter.

Bright and dark soliton solutions in growing Bose-Einstein condensates

This paper develops the Hirota method carefully for applying into the growing model of quasi-one-dimensional Bose Einstein condensations with attractive and repulsive interaction, respectively. After a tedious calculation it obtains the exact bright and dark soliton solutions analytically. It shows that the growing model has the important effect on the soliton amplitude and the time-dependent potential only contributes to the phase and phase velocity. A detailed analysis for the asymptotic behaviour of two-soliton solutions shows that the collision of two soliton is elastic.

Effect of dark soliton on the spectral evolution of bright soliton in a silicon-on-insulator waveguide

The spectral evolution of bright soliton in a silicon-on-insulator optical waveguide is numerically simulated using the split-step Fourier method.The power and input chirp of the dark soliton and the second-order dispersion are varied to investigate the effect of dark soliton on the spectrum of bright soliton.The simulations prove that the dark soliton modifies the spectral shape of the bright soliton.Further,the variation in the power of dark soliton affects the splitting of bright soliton.Furthermore,the chirped dark soliton can improve the spectral width and flatness.The variation in the dispersion of dark soliton modifies the phase matching of the bright soliton and the dispersive wave emission,thereby affecting the spectral evolution.

Self—Steepening and Thired—Order Dispersion Induced Optical Solitons in Fiber

Usually,one considers only the group velocity dispersion(GVD)-and self-phase modulation(SPM)-induced solitons in optic soliton communication while other higher order effects such as the third-order dispersion(TOD),self-steepening(SS),and stimulated Raman scattering are considered only perturbatively,In this paper,we study the existence of the TOD-and SS-induced soliton solutions.The existence conditions of the TOD-and SS-induced bright and dark solitons are quite different from those of the GVD-and SPM-induced solitons.

Stable soliton propagation in a coupled (2+1) dimensional Ginzburg-Landau system

A coupled(2+1)-dimensional variable coefficient Ginzburg-Landau equation is studied.By virtue of the modified Hirota bilinear method,the bright one-soliton solution of the equation is derived.Some phenomena of soliton propagation are analyzed by setting different dispersion terms.The influences of the corresponding parameters on the solitons are also discussed.The results can enrich the soliton theory,and may be helpful in the manufacture of optical devices.

Bright and dark optical solitons in the nonlinear Schrdinger equation with fourth-order dispersion and cubic-quintic nonlinearity

By the use of an auxiliary equation, we find bright and dark optical soliton and other soliton solutions for the higher-order nonlinear Schrodinger equation (NLSE) with fourth-order dispersion (FOD), cubic-quintic terms, self-steepening, and nonlinear dispersive terms. Moreover, we give the formation condition of the bright and dark solitons for this higher-order NLSE.

Controlling the amplitude of soliton in a growing Bose-Einstein condensate by means of Feshbach resonance

By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose-Einstein condensate （BEC）. It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases （increases） for the BEC growing coefficient Ω 〈 0 （Ω 〉 0）. Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment.

Current-induced magnetic soliton solutions in a perpendicular ferromagnetic anisotropy nanowire

Magnon density distribution can be affected by the spin-transfer torque in a perpendicular ferromagnetic anisotropy nanowire. We obtain the analytical expression for the critical current condition. For the cases of below and above the critical value, the magnon density distribution admits bright and dark soliton states, respectively. Moreover, we discuss two-soliton collision properties that are modulated by the current. Each magnetic soliton exhibits no changes in both velocity and width before and after the collision.

Spatiotemporal binary interaction and designer quasi-particle condensates

We introduce a new integrable model to investigate the dynamics of two component quasi-particle condensates with spatiotemporal interaction strengths. We derive the associated Lax pair of the coupled Gross-Pitaevskii （GP） equation and construct matter wave solitons, We show that the spatiotemporal binary interaction strengths not only facilitate the stabilization of the condensates, but also enables one to fabricate condensates with desirable densities, geometries, and properties, leading to the so-called ＂designer quasi-particle condensates＂.

Exact soliton solutions in anisotropic ferromagnetic wires with Dzyaloshinskii–Moriya interaction

We theoretically investigate the exact soliton solutions of anisotropic ferromagnetic wires with Dzyaloshinskii–Moriya interaction. For example, we give the bright and black soliton solutions. From these results we find that the Dzyaloshinskii–Moriya interaction affects the existence region of soliton, spin-wave transport, and soliton dynamic properties. As the Dzyaloshinskii–Moriya interaction grows, the soliton width is widened, which provides a way to control the soliton dynamics.