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We study the topological phase of bright soliton with arbitrary velocity under the self-steepening effect. Such topological phase can be described by the topological vector potential and effective magnetic field. We find that the point-like magnetic fields corresponds to the density peak of such bright solitons, where each elementary magnetic flux is {\pi}. Remarkably, we show that two bright solitons can generate an additional topological field due to the phase jump between them. Our research provided the possibility to use bright solitons to explore topological properties.

Solitons in multi-component Bose-Einstein condensates have been paid much attention, due to the stability and wide applications of them. The exact soliton solutions are usually obtained for integrable models. In this paper, we present four families of exact spin soliton solutions for non-integrable cases in spin-1 Bose-Einstein Condensates. The whole particle density is uniform for the spin solitons, which is in sharp contrast to the previously reported solitons of integrable models. The spectrum stability analysis and numerical simulation indicate the spin solitons can exist stably. The spin density redistribution happens during the collision process, which depends on the relative phase and relative velocity between spin solitons. The non-integrable properties of the systems can bring spin solitons experience weak amplitude and location oscillations after collision. These stable spin soliton excitations could be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose-Einstein condensates., 8 pages, 6 figures

Modulational instability has been used to explain the formation of breather and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. We develop a method to derive general forms for Akhmediev breather and rogue wave solutions in a $N$-component nonlinear Schr��dinger equations. The existence condition for each pattern is clarified clearly. Moreover, the general multi-high-order rogue wave solutions and multi-Akhmediev breather solutions for $N$-component nonlinear Schr��dinger equations are constructed. The results further deepen our understanding on the quantitative relations between modulational instability and homoclinic orbits solutions., 30 pages

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr��dinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the special limitation on the wave vectors. As an application, we exhibit the first, second-order rogue wave solution and the superposition of them by computer plotting. We find the distribution patterns for vector rogue waves are much more abundant than the ones for scalar rogue waves, and also different from the ones obtained with the constrain conditions on background fields. The results further enrich and deep our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids., 9 pages, 7 figures

We investigate the localized waves of the coupled two-mode nonlinear Schr\"{o}dinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov-Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal-spatial structures. The phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Our results have implications in such diverse fields as Bose-Einstein condensate, nonlinear fibers and super fluids., Comment: 5 pages, 6 figures

In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and multi-dark soliton solutions for multi-component coupled NLS with defocusing case and mixed focusing and defocusing case. Some exact single and two-dark solitons of three-component NLS equation are shown by plotting the picture., Comment: 14 pages, 4 figures

Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference pattern is determined by the relative velocity of the solitons, and the temporal pattern behavior is determined by the peak amplitudes and the kinetic energy of the solitons. Analytical expressions for the periods of the interference patterns are obtained. A method for classifying the nonlinearity of many nonlinear systems is proposed. As an example, we discuss possibilities to observe these properties of solitons in a nonlinear planar waveguide., 5pages, 4 figures

We present a simple representation for arbitrary-order rogue wave solution and study on the trajectories of them explicitly. We find that the global trajectories on temporal-spatial distribution all look like "X" shape for rogue waves. Short-time prediction on rogue wave can be done through measuring the information contained in the initial perturbation twice., Research paper, 6 pages, 6 figures

We study localized wave on continuous wave background analytically in a nonlinear fiber with higher order effects such as higher order dispersion, Kerr dispersion, and stimulated inelastic scattering. We present an exact rational W-shaped soliton solutions, whose structural properties depend on the frequency of the background field. The hump value increase with the decrease of the background frequency in the certain regime. The highest value of the W-shaped soliton can be nine times the background's, and the distribution shape is identical with the one of well-known eyes-shaped rogue wave with its maximum peak. The numerical stimulations indicate that the W-shaped soliton is stable with small perturbations., Comment: 5 pages, 4 figures

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr��dinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones in single component systems. The distribution shape can be quadrilateral, triangle, and line structures through varying the proper initial excitations given by the exact analytical solutions. Moreover, six fundamental rogue wave can emerge on the distribution for second-order vector rogue wave, which is similar to the scalar third-order ones. The distribution patten for vector ones are much abundant than the ones for scalar rogue waves. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids., 5 pages, 4 figures

We investigate the localized waves of the coupled two-mode nonlinear Schr��dinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov-Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal-spatial structures. The phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Our results have implications in such diverse fields as Bose-Einstein condensate, nonlinear fibers and super fluids., 5 pages, 6 figures

In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and multi-dark soliton solutions for multi-component coupled NLS with defocusing case and mixed focusing and defocusing case. Some exact single and two-dark solitons of three-component NLS equation are shown by plotting the picture., 14 pages, 4 figures

The exact solitonic solutions of the one-dimensional nonlinear Schrodinger 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.