Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.     

On exact N-loop soliton solution to nonlinear coupled dispersionless evolution equations

We investigate some nonlinear coupled dispersionless evolution equations (NLCDEE) modelling the dynamics of a current-fed string within an external magnetic field in 2D-space. Using a blend of transformations of independent variables, we derive from the previous equations a Schäfer-Wayne short pulse equation (SWSPE). By means of a transformation back to the original independent variables, we find the N-loop soliton solution to the coupled equations. We give some detail on the scattering behavior of two-loop solitons.     

Short Envelope Solitons in Nonconservative Media

We consider the dynamics of short envelope solitons within the framework of the third-order nonlinear Schrödinger equation with allowance for both linear losses and pumping by an external wave field. An equation for the soliton amplitude is derived. The stationary value of the soliton amplitude is found.     

Effects of Finite Magnetic Field and Ion Motion on Solitary Space Charge Waves

A KDV equation is derived to describe the weakly nonlinear behaviour of electron plasma waves propagating along a plasma-filled cylindrical waveguide immersed in an external strong but finite axial magnetic field. Solution of the KDV equation shows that the soliton properties depend significantly on the strength of external magnetic field as well as on ion motion.     

Damping-like effects in Heisenberg spin chain caused by the site-dependent bilinear interaction

We investigate a continuous Heisenberg spin chain equation which models the local magnetization in ferromagnet with time-and site-dependent inhomogeneous bilinear interaction and timedependent spin-transfer torque.By establishing the gauge equivalence between the spin chain equation and an integrable generalized nonlinear Schr?dinger equation,we present explicitly a novel nonautonomous magnetic soliton solution for the spin chain equation.The results display how the dynamics of the magnetic soliton can be controlled by the bilinear interaction and spin-polarized current.Especially,we find that the site-dependent bilinear interaction may break some conserved quantity,and give rise to damping-like effect in the spin evolution.     

Lattice soliton equation hierarchy and associated properties

As a new subject, soliton theory is shown to be an effective tool for describing and explaining nonlinear phenomena in nonlinear optics, super conductivity, plasma physics, magnetic fluid, etc. Thus, the study of soliton equations has always been one of the most prominent events in the field of nonlinear science during the past few years. Moreover, it is important to seek the lattice soliton equation and study its properties. In this study, firstly, we derive a discrete integrable system by using the Tu model. Then, some properties of the obtained equation hierarchies are discussed.     

Effect of Second Nonthermal Ion on the Characteristics of Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Variable Dust Charge

The nonlinear dust acoustic solitary waves in a magnetized dusty plasma with nonthermal ions and variable dust electric charge is studied analytically. Using reductive perturbation method the Zakharov‐Kuznetsov (ZK) equation is derived and effect of nonthermal coefficient, external magnetic field, and variable dust electric charge on the amplitude and width of soliton in dusty plasma is investigated. With increasing the rate of dust charge variation with respect of plasma potential, the amplitude of generated solitary waves in magnetized dusty plasma increases to a constant magnitude while its width decreases. Increasing the nonthermal ions coefficient leads to a noticeable decrease in the amplitude of solitons while the width of soliton increases. The amplitude of generated solitary waves in such a dusty plasma is independent of applied external magnetic field but we will have more localized solitons with increasing the external magnetic field strength. It is found that solitons are strongly influenced by the direction of external magnetic field. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear sigma model and the origin of geometric frustration on curved manifolds

Classical Heisenberg spins considered on an elastic two-dimensional curved manifold in the continuum limit correspond to the nonlinear σ model. If the corresponding Euler-Lagrange (EL) equations support a soliton solution, a mismatch of length scales induces geometrical frustration in the region of the soliton which is relieved by a deformation of the manifold in the region of the soliton. We illustrate the origin of this elastic effect in four different cases: (i) A single soliton on a circular cylinder with anisotropic spin-spin coupling, (ii) a soliton lattice on a circular cylinder with isotropic spin-spin coupling, (iii) a single soliton on an elliptic cylinder, and (iv) a circular cylinder in an external axial magnetic field. For the first three cases the EL equation is the sine-Gordon equation while for the last case it is the double sine-Gordon equation. Geometrical frustration results whenever the solution of the EL equation does not satisfy the self-dual equations of Bogomol’nyi which are a necessary condition to reach the minimum energy configuration in each homotopy class.     

Nonlinear Dynamics of Circularly Polarized Laser Pulse Propagating in a Magnetized Plasma with q ‐Nonextensive Velocity Distributions

The nonlinear dynamics of a circularly polarized laser pulse propagating in magnetized plasma contains hot nonextensive q ‐distributed electrons and ions is studied theoretically. A nonlinear equation which describes the dynamics of the slowly varying amplitude electromagnetic wave is obtained using the relativistic two‐fluids model. Some nonlinear phenomena include modulational instability, self‐focusing, soliton formation, and longitudinal and transversal evolutions of laser pulse in nonextensive plasma medium are investigated. Results show that the nonextensivity of particles can substantially change the nonlinearity of medium. The external magnetic field enhances the modulation instability growth rate of right‐hand polarization wave but for the left‐hand polarization the growth rate decreases. The spot size of the laser pulse is strongly affected by the plasma nonextensivity. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrödinger equation

Hamiltonian equations are formulated in terms of collective variables describing the dynamics of the soliton of an integrable nonlinear Schrödinger equation on a 1D lattice. Earlier, similar equations of motion were suggested for the soliton of the nonlinear Schrödinger equation in partial derivatives. The operator of soliton momentum in a discrete chain is defined; this operator is unambiguously related to the velocity of the center of gravity of the soliton. The resulting Hamiltonian equations are similar to those for the continuous nonlinear Schrödinger equation, but the role of the field momentum is played by the summed quasi-momentum of virtual elementary system excitations related to the soliton.     

匀强磁场对水中气泡运动的影响

基于Rayleigh-Plesset方程, 考虑极性水分子在均匀磁场运动受到磁场力作用, 根据能量守恒建立了外磁场作用下单气泡运动的控制方程, 并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析. 结果表明: 随磁场强度的增强, 附加压强线性增大, 气泡膨胀率降低, 最大半径减小, 气泡坍缩速度下降; 外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.     

Localized Spatial Soliton Excitations in (2+1)-Dimensional NonlinearSchrödinger Equation with Variable Nonlinearity and an ExternalPotential

We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrödinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota's binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized solutions of different but desired forms. For some specific external potentials and nonlinearity coefficients, we discuss features of the corresponding (2+1)-dimensional multisolitonic solutions, including ring solitons, lump solitons, and soliton clusters.     

Nonlinear Dynamics of Wave Fields in Nonresonant Media: From Envelope Solitons toward Video Solitons

We analyze a new class of soliton solutions for a wave field, which describes propagation of soliton-like structures of a circularly polarized electromagnetic field comprising a finite number of field-oscillation periods in a transparent nonresonant medium. The considered solutions feature a smooth transition from the soliton solutions of Schröodinger type, which correspond to long pulses with a large number of field oscillations, to extremely short, virtually single-cycle video pulses. We show that such solutions can also be important for linearly polarized laser fields. The structural stability of few-optical-cycle solitons is demonstrated numerically, including the case of their collision. Based on stability analysis and with allowance for the genealogic relation between the obtained wave solitons and the solitons of the nonlinear Schröodinger equation, we argue that the former solitons can play the same fundamental role in the nonlinear dynamics of the considered wave fields. In particular, it is shown by numerical simulations that the few-optical-cycle solutions turn out to be the basic elementary components of such a dynamical process as the temporal compression of an initially long pulse to a pulse of very short duration. In this case, the minimum duration of a compressed pulse is determined by soliton structures of about minimal duration.     

Dynamics of the soliton instability in the easy-plane ferromagnetic chain

We present results on the nonlinear dynamics of a realistic classical easy-plane ferromagnetic chain in an external magnetic field, concerning in particular the dependence of soliton solutions on the strength of the single-ion anisotropy. After giving two exact static solutions, slowly moving permanent profile solutions are investigated. The velocity dependent contribution to the energy as well as the amplitude of the out-of-plane distortion of these solutions is shown to diverge when the Magyari-Thomas-Kumar instability of the static Sine-Gordon soliton is approached. The dynamic origin of this instability is shown to be an unstable behaviour of the soliton towards spontaneous motion instead of a soft mode.     

Magnetization dynamics of an integrable model of 3D ferromagnetic spin system

We formulate the dynamical equation of a 3 dimensional Heisenberg ferromagnetic (FM) spin system with bilinear and anisotropic interactions in the semiclassical limit. In the continuum limit the dynamics is found to be governed by a (3+1) dimensional nonlinear Schrödinger equation. We check the integrability of the dynamics by constructing Lax pair of operators. To express the nonlinear spin excitations in terms of magnetic soliton, we use Darboux transformation(DT) and Hirota bilinearization procedure .     

Quantum Phenomena in a Classical Model

This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles.     

Electromagnetic soliton propagation in an anisotropic Heisenberg helimagnet

We study the nonlinear spin dynamics of Heisenberg helimagnet under the effect of electromagnetic wave (EM) propagation. The basic dynamical equation of the spin evolution governed by Landau–Lifshitz equation resembles the director dynamics of the twist in a cholestric liquid crystal. With the use of reductive perturbation technique the perturbation is invoked for the spin magnetization and magnetic field components of the propagating electromagnetic wave. A steady-state solution is derived for the weakly nonlinear regime and for the next order, the components turn around s plane perpendicular to the propagation direction. It is found that as the electromagnetic wave propagates in the medium, both the magnetization and magnetic field modulate in the form of kink soliton modes by introducing amplitude fluctuation in the tail part of the same.     

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.     

Nonlinear localization of excitations and the dynamics of solitons in self-modulated systems

The nonlinear dynamics of systems with a spatially periodic ground state was studied. The dynamics of kinks against the background of a periodic soliton structure was considered for the example of the sine-Klein-Gordon model that described a fluxon lattice in a long Josephson contact in an external magnetic field and an incommensurate structure of a surface atomic layer or adatom chains on the surface of a crystal. The velocity of moving kinks was shown to be bounded from above and from below if the ground state was spatially periodic.     

Nonlinear spin excitations in a classical Heisenberg anisotropic helimagnet

The nonlinear spin excitations in an anisotropic helimagnet in the presence of a constant magnetic field are investigated in the classical continuum limit. The helical character is introduced into the model, in analogy with the twist in a cholesteric liquid crystal. After deriving a class of spin wave solutions for the stereographic representation of the Landau-Lifshitz equation, in-plane stationary spin configurations are obtained and their stability is analysed. When the external magnetic field is along the anisotropic axis, modulational instability is observed in the spin lattice, and when the external magnetic field is normal to the anisotropic axis, the spin configurations are unstable. The perturbed spin components show fluctuations in the tail region, while the velocity and amplitude of the soliton remain unaltered.