单离子各向异性影响下的一维铁磁链中的孤子

利用行波解法，研究了考虑交换各向异性和单离子各向异性的一维铁磁链，得出椭圆函数波解和孤子解,并讨论了单离子各向异性对椭圆函数波和孤子的影响.研究表明：单离子各向异性对一维铁磁链中椭圆函数波和孤子的激发及其稳定性有显著影响.单离子各向异性不利于易轴铁磁链中椭圆函数波和孤子解的激发，但有利于它们的稳定；而在易平面铁磁链中，单离子各向异性使椭圆函数波和孤子激发变得容易，但不利于它们的稳定.此外，还讨论了单离子各向异性对一维各向同性铁磁链中的孤子激发具有的影响. 关键词： 各向异性 单离子各向异性 孤子 铁磁链     

光诱导准一维光子晶格中离散空间光孤子的相互作用

基于分步束传播法数值分析了离散空间光孤子在准一维光诱 导光子晶格中的相干与非相干相互作用过程. 结果表明: 对于相干孤子, 同相时相互吸引, 反相时相互排斥. 然而, 由于非线性响应的各向异性, 横向排布的非相干孤子会因间隔波导数目的增加而由相互吸引变为相互排斥. 并且, 沿对角方向排布的两个非相干孤子在孤子相 互作用力和布拉格反射的共同影响下, 会呈现出"钟摆式"振荡传输现象. 研究结果有助于进一步理解非线性各向异性对离散孤子相互作用的影响机制, 并为后续实验研究提供理论参考.     

Algebraic soliton in a ferromagnet in the presence of the magnetic field directed along the anisotropy axis

Magnetic solitons in a one-dimensional ferromagnet with easy-plane anisotropy are considered. Algebraic solitons are discussed and the conditions of existence of such solitons are investigated.     

Interaction of solitons with impurities in anisotropic ferromagnetic chains

The interaction of bright solitons with impurities in the on-site anisotropy of a ferromagnetic chain is studied. This type of impurities leads to linear and nonlinear perturbing terms in the corresponding nonlinear Schrödinger equation. We have found static soliton-impurity bound states and considered the conditions for their formation. For large values of the anisotropy the character of the impurities is mainly linear. The interaction of propagating solitons with the impurities is also investigated. We have obtained that the solitons can be transmitted, trapped or reflected. The behavior depends on the soliton velocity and width, magnetic parameters and the impurity strength.     

Ball solitons in kinetics of the first-order magnetic phase transition

The theory of magnetic ball solitons (BS) arising as a result of the energy fluctuations, at the spin–flop transition induced by a magnetic field in antiferromagnets with uniaxial anisotropy, is presented. Such solitons are possible in a wide range of amplitudes and energies, including the negative energy relative to an initial condition. When such antiferromagnet is in a metastable condition, ball solitons are born with the greatest probability if the energy of solitons is close to zero. Evolution of these solitons, at which they develop into macroscopic domains of a new magnetic phase, is analyzed, thus, carrying out full phase reorganization.     

Dipole solitons in nonlocal nonlinear media with anisotropy

We investigate the existence and stability of dipole-mode solitons in two-dimensional models of nonlocal media with anisotropic Kerr nonlinearity analytically and numerically. We obtain the approximate solution of such elliptic dipole solitons by using the variational approximation. The dynamics of such dipole-mode solitons is governed by the eccentricity of both the input beam and the nonlocal response function. We also compute the stability of the solitons by direct numerical simulations. The effects of the anisotropy of the nonlocal response function on the propagation of the dipole beam are also discussed in detail.     

Quadrupolar matter-wave soliton in two-dimensional free space

We study two-dimensional (2D) matter-wave solitons in the mean-field models formed by electric quadrupole particles with long-range quadrupole–quadrupole interaction (QQI) in 2D free space. The existence of 2D matter-wave solitons in the free space was predicted using the 2D Gross–Pitaevskii Equation (GPE). We find that the QQI solitons have a higher mass (smaller size and higher intensity) and stronger anisotropy than the dipole–dipole interaction (DDI) solitons under the same environmental parameters. Anisotropic soliton–soliton interaction between two identical QQI solitons in 2D free space is studied. Moreover, stable anisotropic dipole solitons are observed, to our knowledge, for the first time in 2D free space under anisotropic nonlocal cubic nonlinearity.     

Discrete and dipole-mode gap solitons in higher-order nonlinear photonic lattices

We investigate the formation of fundamental discrete solitons and dipole-mode gap solitons in triangular photonic lattices imprinted in photorefractive nonlinear media. These lattices are strongly affected by the photorefractive anisotropy, resulting in orientation-dependent refractive index structures with reduced symmetry. It is demonstrated that two different orientations of the lattice wave enable the formation of fundamental discrete solitons in the total internal reflection gap. Furthermore, it is shown that one lattice orientation additionally supports dipole-mode solitons in the Bragg reflection gap. The experimental results are corroborated by numerical simulations using the full anisotropic model. PACS 42.65.Tg; 42.65.Wi; 42.70.Qs     

负性介电各向异性向列相液晶中空间光孤子的理论研究

对非局域非线性介质向列相液晶中介电各向异性为负时的情况进行了研究.理论研究表明,负性介电各向异性的向列相液晶具有负的非线性系数.文中给出了其空间非局域响应特征宽度和非线性系数的表达式,并求出了其非局域响应函数;其次,用数值计算的方法给出了其空间孤子的传输结果.最后,研究了光束功率和偏置电压的改变对负性介电各向异性向列相液晶中光束传输的影响,发现偏置电压的改变会导致光束在负性介电各向异性液晶中形成孤子所需的临界功率发生改变.     

Stability of solitons in nonlinear composite media

An analysis is made of the dynamic stability of soliton solutions of the Hamilton equations describing plane waves in nonlinear elastic composite media in the presence and absence of anisotropy. In the anisotropiccase two two-parameter soliton families, fast and slow, are obtained in analytic form; in the absence of anisotropy there is a single three-parameter soliton family. It is shown that solitons from the slow family in an anisotropic composite and solitons in an isotropic composite are dynamically stable if their velocities lie in a certain range known as the range of stability. The analysis of stability is based on the spectral properties of the “linearized Hamiltonian” ?. It is shown that the operator ? is positively semidefinite on some linear subspace of the main solution space from which stability follows. Problems of instability of the fast soliton family in the anisotropic case and representatives of soliton families whose velocities lie outside the range of stability in the presence and absence of anisotropy are discussed.     

Dark solitons in ferromagnetic chains with first- and second-neighbor interactions

We present a study of the ferromagnetic spin chain with both first- and second-neighbor interactions. We obtain the condition for the appearance and stability of bright and dark solitons for arbitrary wave number in the Brillouin zone. The influence of the second-neighbor interaction and the anisotropy on the soliton properties is considered. The scattering of dark solitons from point defects in the discrete spin chain is investigated numerically.     

Two-dimensional bright solitons in dipolar Bose-Einstein condensates

We analyze the physics of bright solitons in 2D dipolar Bose-Einstein condensates. These solitons, which are not possible in short-range interacting gases, constitute the first realistic proposal of fully mobile stable 2D solitons in ultracold gases. In particular, we discuss the necessary conditions for the existence of stable 2D bright solitary waves by means of a 3D analysis of the lowest-lying excitations. We show that the anisotropy of the dipolar potential is crucial, since sufficiently large dipolar interactions can destabilize the 2D soliton. Additionally, we study the scattering of solitary waves, which, contrary to the contact-interacting case, is inelastic and could lead to fusion of the waves. Finally, the experimental possibilities for observability are discussed.     

Topological and dynamical excitations in a classical 2D easy-axis Heisenberg model

The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of applicability of the continuum approach are discussed. Received 22 August 2000     

Dynamical toroidal Hopfions in a ferromagnet with easy-axis anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.     

负性向列相液晶中1+1维空间光孤子:微扰法

利用微扰法对负性向列相液晶中的1+1维空间光孤子进行了系统性的研究, 得到了近似解析孤子解.通过数值迭代, 发现只有当非局域程度大于某一临界值时孤子才能存在.近似解析解即使在一般非局域程度下和数值解也符合得较好. 为讨论孤子的稳定性, 进行了线性稳定性分析, 发现孤子均是稳定的, 数值模拟进一步证实了线性稳定性分析的结果.     

Anisotropic photonic lattices and discrete solitons in photorefractive media

We study experimentally two-dimensional periodic photonic lattices optically imprinted in photorefractive nonlinear media, and explore the effect of anisotropy on the induced refractive-index patterns. The orientation anisotropy is demonstrated by comparing square and diamond lattices, while the polarization anisotropy is shown to distinguish ordinarily and extraordinarily polarized light. In particular, the extraordinarily polarized lattice induces much stronger refractive-index modulation for the same conditions. Finally, we exploit the photorefractive anisotropy to generate a quasi-one-dimensional refractive-index pattern for the observation of two-dimensional solitons and corroborate these experiments by numerical simulations. PACS 42.65.Tg; 42.65.Wi     

Large-radius dynamic topological solitons in uniaxial ferromagnets

In thin ferromagnetic films with perpendicular anisotropy, there exist stable large-radius dynamic topological solitons, which are stabilized owing to conservation of the orbital angular momentum of the magnetization field. The solitons can also exist if the projection of the total spin moment of the magnet onto the easy axis is not conserved, i.e., in the absence of pure uniaxial symmetry of the model. Even in the pure uniaxial case, the magnetization distribution in a soliton with a sufficiently large radius differs significantly from centrosymmetric.     

A new class of nodal stationary states in a 2D Heisenberg Ferromagnet

A new class of nodal topological excitations in a 2D Heisenberg model is studied. The solutions correspond to a nodal singular point of the gradient field of the azimuthal angle. An analytical solution is found for the isotropic case. The effect of in-plane exchange anisotropy is studied numerically. This results in solutions which are analogues of the conventional out-of-plane solitons in 2D magnets.     

Generation of acoustic solitons by a single-mode electromagnetic field

Mechanisms of acoustic pulse generation by a single-mode electromagnetic field propagating in a photoelastic material are analyzed. The anisotropy induced by acoustic excitations in an isotropic medium leads to nonlinear coupling between the polarization components of a single-mode electromagnetic field. For different conditions, it is shown that the acoustic-electromagnetic wave interaction due to mixing of the polarization components of light and acoustic waves can give rise to soliton-like coherent acoustic excitations in a thin crystal plate. When spatial dispersion is ignored, the governing system of equations for unidirectional acoustic solitons can be reduced to an integrable model. It is shown that qualitatively different scenarios of formation of acoustic solitons are possible, depending on the directions of deformation and field polarization.     

On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry

We study the Heisenberg model on cylindrically symmetric curved surfaces. Two kinds of excitations are considered. The first is given by the isotropic regime, yielding the sine-Gordon equation and π solitons are predicted. The second one is given by the XY model, leading to a vortex turning around the surface. Helical states are also considered, however, topological arguments cannot be used to ensure its stability. The energy and the anisotropy parameter which stabilizes the vortex state are explicitly calculated for two surfaces: catenoid and hyperboloid. The results show that the anisotropy and the vortex energy depends on the underlying geometry.