Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e.Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.``     

Multifrequency gap solitons in nonlinear photonic crystals

We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective frequency components or stabilize their excitations. These MFGSs form a new class of stable gap solitons.     

Modulational instability and gap solitons in periodic ferromagnetic films

The modulational instability and gap solitons are theoretically studied in the ferromagnetic films under a periodic magnetic field. By multiple scale expansion, the envelope soliton solutions are obtained naturally. Due to the periodic modulation of dispersion, the solitons may be pushed into the gap region. For the easy-axis magnetic film, the red-shift of frequency leads to a modulational instability in the bottom of band and generates a bright gap soliton. For the easy-plane case, the blue-shift leads to an instability in the top of band and a dark gap soliton emerges. The weak damping produces an attenuation factor and a small oscillation.     

A model of Wigner liquid

A two-dimensional low-density system of charge carriers with strong Coulomb interaction, which can lead to the appearance of a short-wavelength soft mode (precursor of crystallization) is examined. This system provides elementary excitations of two types: Fermi excitations and Bose excitations with a gap in the spectrum. The latter excitations are similar to rotons in superfluid helium. A model involving the Fermi liquid and the soft mode is proposed, and interaction of different excitations with each other is described phenomenologically as in the Landau theory of Fermi liquid. By solving the derived equations, it was found that, as the temperature increases, the effective mass of Fermi excitations decreases and the gap in the Bose excitation spectrum increases.     

Folded Localized Excitations of the (2 + 1)-Dimensional Broer-Kaup Equation

Considering that the multi-valued (folded) localized excitations may appear in many (2 1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2 1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.     

Soliton excitations in a polariton condensate with defects

To study soliton excitations in a polariton condensate with defects, we use the Gross-Pitaevskii equation and its hydrodynamic form. An extra term is added to take into account the non-equilibrium nature of the polariton condensate and the presence of defects. The reductive perturbation method transforms these hydrodynamic equations into a modified Korteweg-de Vries equation in the long wavelength limit. We linearize this equation and study the soliton linear excitations.We give an analytic expression of traveling excitations using the variation of constants method. In the more general form,we show numerically that the excitations are oscillations, i.e., the amplitude and the width of the dark soliton oscillate simultaneously but in an opposite way.     

Folded Localized Excitations of the （2＋1）-Dimensional Broer-Kaup Equation

Considering that the multi-valued (folded) localized excitations may appear in many (2 1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2 1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.     

Kink Pair in Hydrogen Bonded Systems with Symmetric Double-Well Potential

In hydrogen-bonded systems with a symmetric double-well potential, using the variational method, we study the nonlinear excitations and motion of the solitons in the presence of the optical mode of the heavy ion sublattice, based on a new two-component soliton model. We give the equations of motion and soliton-solutions in such a case. Based on these results we calculate further the energy, the momentum and the effective mass of the kink pair.     

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.     

Na掺杂反式聚乙炔中的孤子晶格的能谱与电子束缚态

从离散的ＳＳＨ模型出发，考虑了链内的电子相互作用，以及由杂质和周围链上的荷电孤子产生的库仑势的影响，探讨了各种掺杂浓度的反式聚乙炔中孤子晶格的能谱与电子束缚态。计算结果表明：在孤子晶格的能谱中，在价带底有两条定域能级，在导带顶存在着多个电子束缚态，随掺杂浓度的升高，束缚态的局域性减弱，禁带中的孤子能级形成孤子能带。当掺杂浓度高达１６．６７％时，所有的电子束缚态都消失，转变为扩展态。孤子晶格的禁带宽度随着掺杂浓度的增加而增大，最高占据态与导带底之间的能隙则随之逐渐减小。孤子能带底与价带顶之间的能隙在临界浓度附近有一极大值。还讨论了电子－电子相互作用对孤子晶格能谱的影响。 关键词：     

具有二阶和三阶非线性一维光子晶体中的耦合模孤子

研究同时具有二阶和三阶非线性的一维光子晶体中的耦合孤子动力学.从Maxwell方程出发,利用多重尺度法,导出了光学整流场与两个基频电场包络的非线性耦合模方程组,给出了耦合模方程组的孤子解.结果表明,由于二阶非线性导致的光学整流场对基频电场有调制作用,使得两个基频电场分量可以呈现为亮孤子亮孤子、暗孤子暗孤子及亮孤子-暗孤子对 当两个基频电场的振动频率趋于光子晶体频带的带边频率时,光学整流场消失     

Gap soliton in a waveguide array with a saturating defocusing nonlinearity

We investigate radiation of the solitary waves in the first band gap of the waveguide array with a defocusing nonlinearities of different types (Kerr nonlinearity and saturating nonlinearity). We confirm recent findings that gap solitons (GSs) are unstable for their eigenfrequencies around the middle of the band gap for Kerr nonlinearity. The instability is mediated by four-wave mixing process and appears in the form of radiation of solitons into mode continua of the upper and lower bands. We find that this soliton radiation is reduced (and even suppressed completely) in case of a saturating nonlinearity, resulting in substantial stabilization of the GSs.     

The Exact Solutions of Some (2 + 1)-Dimensional Integrable Systems

The equivalence of three (2 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.     

Dynamical Stability of Gap Soliton of One-Dimensional Condensate in Optical Lattices with Strong Interatomic Interaction

By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose- Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.     

The Exact Solutions of Some (2+1)-Dimensional Integrable Systems

The equivalence of three (2+1)-dimensional soliton equations is proved, and the quite general solutions with some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many special types of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutions are obtained.     

A numerical investigation of the non-linear equation of motion of the one dimensional anti-ferromagnet

In this paper we study the soliton excitations in a classical one dimensional anisotropic antiferromagnet in an external magnetic field using a numerical approach to solve the non-linear equations of motion.     

Raman gap solitons

We show that an intense pump pulse, detuned far from the Bragg resonance of a nonlinear periodic structure, can excite a gap soliton at a wavelength within the band gap that corresponds to the Raman shift of the medium. This Raman gap soliton is a stable, long-lived, quasistationary excitation that exists within the grating even after the pump pulse has passed. We find both stationary solitons as well as slow Raman gap solitons with velocities as low as 1% of the speed of light. The predicted phenomena should be observable in fiber Bragg gratings and other nonlinear photonic band gap structures.     

Observation of in-band lattice solitons

We report the first experimental and theoretical demonstrations of in-band (or embedded) lattice solitons. Such solitons appear in trains, and their propagation constants reside inside the first Bloch band of a square lattice, different from all previously observed solitons. We show that these solitons bifurcate from Bloch modes at the interior high-symmetry X points within the first band, where normal and anomalous diffractions coexist along two orthogonal directions. At high powers, the in-band soliton can move into the first band gap and turn into a gap soliton.     

Nonlinear dynamics of incommensurate surface layers

We describe analytically the nonlinear dynamics of the incommensurate surface layer ("self-modulated" system) with a spatially periodical structure. In the framework of the Frenkel-Kontorova model the nonlinear excitations of the periodic soliton lattice, such as moving additional kinks and gap solitons, are investigated.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼