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.     

Analytical study of stationary soliton excitations in diamond-structure chain with quartic anharmonicity

This work analytically study soliton excitations in an one-dimensional chain with the same mass but two alternating force constants between the nearest neighbors by means of multiple scales method plus quasi-discrete approximation. This model simulates a row of atoms in the 〈111〉 direction of a diamond-structure type of crystals. The explicit expressions of the stationary soliton solutions are obtained at some special wave vectors of the carrier wave (q=±π/a for acoustic mode and q=0, ±π/a for optical mode). The configuration of the atomic displacements of this model is different from that of diatomic chain with quartic anharmonicity.     

Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based on Nagatani's model [Nagatani T 1998 Physica A 261 599] is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink--antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.     

Nonautonomous solitons in the continuous wave background of the variable-coefficient higher-order nonlinear Schro¨dinger equation

We reduce the variable-coefficient higher-order nonlinear Schrdinger equation (VCHNLSE) into the constantcoefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.     

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 Schro¨dinger equations.Moreover,the Bogoliubov equation shows that there exists stable dark soliton in specific situations.Our results open up new ways in considerable experimental interest for the quantum control of multi-component Bose-Einstein condensates.     

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.     

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates.It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions.It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.     

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

<正>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.     

The interaction of in-band and in-gap lattice soliton trains in optically induced two-dimensional photonic lattices

We demonstrate the coherent interactions of lattice soliton trains,including in-band solitons (IBSs) and gap soliton trains (GSTs),in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity.It is revealed that the π-staggered phase structures of the lattice soliton trains will lead to anomalous interactions.Solely by changing their initial separations,the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained.The 'negative refraction' effect of the soliton trains on the interaction is also discussed.Moreover,two interacting IBSs can merge into one GST when attraction or energy transfer happens.     

The Critical Properties of a Modulated Quantum sine—Gordon Model

A new procedure of trial variational wave functional is proposed for invostigating the mass reuormalizationand the local structure of the ground state of a one-dimensional quantum sine-Gorrdonm model with linear spatial modu-lation, whose ground state differs from that without modulation. Thc phase diagram obtained in parameters (αA 2,β2)plane shows that the vertical part of the boundary between soliton lattice phase and iucommensurate (IC) phase withvanishing gap sticks at β2 = 4, the IC phase can only appear forβ2 ＞ 47r and thc IC phase regime is enlarged withincreasing spatial modulation in the case of definite parameter αA-2. The transition is of the continuous type on thevertical part of the boundary, while it is of the first order on the boundary forβ2 ＞ 47r.     

层状耦合约瑟夫森双结中的孤子解

基于Sakai-Bodin-Petersen理论，我们求解了对称的双约瑟夫森结的耦合非线性方程组．结果表明，线性化方程组的同相和反相解所对应的两种磁通运动模式也存在于原始的非线性方程组的解中，同时非线性方程组独有的位相锁定的扭折（kinks）形式的磁通运动在低能情况下会演化为孤子解．     

Controlling the amplitude of soliton in agrowing 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.     

Nonlinear chiral models: Soliton solutions and spatio-temporal chaos

Nonlinear effective Lagrangian models with a chiral symmetry have been used to describe strong interactions at low energy, for a long time. The Skyrme model and the chiral quark-meson model are two such models, which have soliton solutions which can be identified with the baryons. We describe the various kinds of soliton states in these nonlinear models and discuss their physical significance and uses in this review. We also study these models from the view point of classical nonlinar dynamical systems. We consider fluctuations around theB=1 soliton solutions of these models (B, being the baryon number) and solve the spherically symmetric, time-dependent systems. Numerical studies indicate that the phase space around the Skyrme soliton solution exhibits spatio-temporal chaos. It is remarkable that topological solitons signifying stability/order and spatio-temporal chaos coexist in this model. In contrast with this, the soliton of the quark-meson model is stable even for large perturbations.     

Soliton Solutions and Interaction Between a Line Soliton and a y-Periodic Soliton in Generalized (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation

Using the variable separation approach, many types of exact solutions of the generalized (2 1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.     

Soliton Solutions and Interaction Between a Line Soliton and a y-Periodic Soliton in Generalized （2W1）-Dimensional Nizhnik-Novikov-Veselov Equation

Using the variable separation approach, many types of exact solutions of the generalized (2 1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.     

光折变有机聚合物中的双色光空间孤子

对光折变有机聚合物中的双色光空间孤子进行了理论分析,证明双色信号光的两个频率成分相互作用可以在折射率改变为正的光折变有机聚合物中形成暗暗和亮暗空间孤子,在折射率改变为负的光折变有机聚合物中形成亮亮和亮暗空间孤子。与单色光孤子的情况不同,对于双色光孤子情况,通过与一形成暗孤子的频率成分相互作用,另一频率成分在折射率改变为正的有机聚合物中也可形成亮孤子;通过与一形成亮孤子的频率成分相互作用,另一频率成分在折射率改变为负的材料中也可形成暗孤子。     

Cusped Solitons and Loop-Solitons of Reduced Ostrovsky Equation

The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of cusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-calledloop-solitons of the Ostrovsky equation.     

Boiti-Leon-Pempinelli系统的新变量分离解及其方形孤子和分形孤子

利用拓展的Riccati方程映射法，得到了(2+1)维Boiti-Leon-Pempinelli系统新的变量分离 解．根据得到的分离变量解，构造出该系统新型的孤子结构——方孤子和分形孤子． 关键词： Boiti-Leon-Pempinelli系统 拓展Riccati映射 方形孤子 分形孤子     

Matter wave solitons in coupled system with external potentials

We present Lax-pair corresponding to the coupled Gross-Pitaevskii equation (CGPE) which governs the evolution of the macroscopic wave function of two components Bose-Einstein condensates trapped in time-dependent harmonic potential. Kinds of soliton solutions can be derived from the Lax-pair through Darboux transformation conveniently. Furthermore, soliton management in two-component Bose-Einstein condensate would be realized base on that the shape and motion of soliton in both components are investigated analytically. Moreover, it is found that there is a transformation existed between the nonautonomous coupled system and Manakov model.     

Nondegenerate soliton solutions in certain coupled nonlinear Schrödinger systems

In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schrödinger type equations through bilinearization procedure. In particular, we consider coupled nonlinear Schrödinger (CNLS) equations (both focusing as well as mixed type nonlinearities), coherently coupled nonlinear Schrödinger (CCNLS) equations and long-wave-short-wave resonance interaction (LSRI) system. We point out that the obtained general form of soliton solutions exhibit novel profile structures than the previously known degenerate soliton solutions corresponding to identical wave numbers in both the modes. We show that such degenerate soliton solutions can be recovered from the newly derived nondegenerate soliton solutions as limiting cases.