共查询到20条相似文献,搜索用时 15 毫秒
1.
Zai-Dong Li 《Annals of Physics》2007,322(8):1961-1971
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. 相似文献
2.
We have simulated numerically the behavior of the one-dimensional, periodic FPU-alpha and Toda lattices to optical and acoustic initial excitations of small--but finite and large amplitudes. For the small-through-intermediate amplitudes (small initial energy per particle) we find nearly recurrent solutions, where the acoustic result is due to the appearance of solitons and where the optical result is due to the appearance of localized breather-like packets. For large amplitudes, we find complex-but-regular behavior for the Toda lattice and "stochastic" or chaotic behaviors for the alpha lattice. We have used the well-known diagnostics: Localization parameter; Lyapounov exponent, and slope of a linear fit to linear normal mode energy spectra. Space-time diagrams of local particle energy and a wave-related quantity, a discretized Riemann invariant are also shown. The discretized Riemann invariants of the alpha lattice reveal soliton and near-soliton properties for acoustic excitations. Except for the localization parameter, there is a clear separation in behaviors at long-time between integrable and nonintegrable systems. 相似文献
3.
《Physics letters. A》1998,241(6):323-328
Using the complex Toda chain we model the asymptotic behavior of the N soliton pulse trains of the nonlinear Schrödinger equation. Stable asymptotic regimes are: (i) asymptotically free propagation of all N solitons; (ii) bound state regime where the N solitons may move quasi-equidistantly (QED); and (iii) various intermediate regimes. Our method allows one to determine analytically the set of initial soliton parameters corresponding to each regime. We list the soliton parameters, which ensure QED propagation of all N solitons since this is important for optical fiber communication. 相似文献
4.
By means of systematic simulations, we study the motion of discrete solitons in weakly dissipative Toda lattices (TLs) with periodic boundary conditions, resonantly driven by a spatially staggered time-periodic (ac) force. A complex set of alternating stability bands and instability gaps, including scattered isolated stability points, is revealed in the parametric plane of the soliton’s velocity and forcing amplitude for a given size of the circular lattice. The analysis is also reported for the circular TL including a single light- or heavymass defect. The stability chart as a whole shrinks and eventually disappears with the increase of the lattice’s size and strength of the mass defect. Qualitative explanations to these findings are proposed. We also report the dependence of the stability area on the initial position of the soliton, finding that the area is largest for some intersite position. For a pair of solitons traveling in opposite directions, there exist regimes where both solitons survive periodic collisions in small-size lattices. 相似文献
5.
首先建立起玻色-爱因斯坦凝聚孤子链的微扰复数Toda链理论,然后深入研究玻色-爱因斯坦凝聚N-孤子间的绝热相互作用,分别通过对二次外势场、周期性外势场和二者叠加的复合外势场所引起的三类微扰,利用微扰的复数Toda链理论给出了解析处理, 并和基于分步傅里叶变换的直接数值方法进行比较,发现微扰的复数Toda链方程能够充分揭示上述三类外势场中的N-孤子链的动力学行为和特征.同时还给出了从孤子链中提取一个或多个局域态的倾斜势场或周期性势场的强度临界值,这可为玻色-爱因斯坦凝聚的实验研究
关键词:
玻色-爱因斯坦凝聚
Gross-Pitaevskii方程
物质波孤子
相互作用 相似文献
6.
《中国物理快报》2016,(11)
We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-onedimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice.It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice.The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter,and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes. 相似文献
7.
Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev-Petviashvili equation 下载免费PDF全文
In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions. 相似文献
8.
Systematic results of collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic
lattices are reported. The generic outcomes are identified for (i) the collision of two identical solitons located in the
corner, at the edge, and in the center of the photonic lattice, and for (ii) the collision of two non-identical corner and
edge solitons located at different distances from the boundaries of the photonic lattice. Depending on the values of the kick
(collision momentum) and of the nonlinear (cubic) gain, the collision scenarios include soliton merging, creation of an extra
soliton, soliton bouncing, soliton spreading, and quasi-elastic (symmetric) interactions. 相似文献
9.
运用约化摄动法研究了非均匀尘埃等离子体中孤子的传播情况. 在低阶近似下, 对于小的、但有限振幅的长波振动, 当分界面不连续变化时,孤子在不连续点的反射波与透射波均可由 KdV 方程来描述, 并给出了低阶近似情况下, 对于小的、但有限振幅的长波振动, 当入射波为单孤子时, 反射孤子与透射孤子的个数及其大小;当分界面是有限长度并连续变化时,对于小的、但有限振幅的长波振动, 尘埃声孤波由KdV型方程来描述,并由此给出了准孤子振幅、传播速度等参量在传播过程中的变化.
关键词:
尘埃等离子体
孤子
KdV方程
约化摄动法 相似文献
10.
Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance 下载免费PDF全文
We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation.What is more,each soliton molecule can be transformed into an asymmetric soliton by changing the parameterφ.In addition,the collision between soliton molecules(or asymmetric soliton)and several soliton solutions is observed.Finally,some related pictures are presented. 相似文献
11.
We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet (dipole), consisting of attractive and repulsive defects with a small distance between them, is considered too. Systematic simulations demonstrate that the triplet provides for superior results, as concerns the capture of a free pulse and creation of a standing optical soliton, in comparison with recently studied traps formed by single and paired defects, as well as the doublet: 2/3 of the energy of the incident soliton can be captured when its velocity attains half the light speed in the fiber (the case most relevant to the experiment), and the captured soliton quickly relaxes to a stationary state. A subsequent collision between another free soliton and the pinned one is examined too, demonstrating that the impinging soliton always bounces back, while the pinned one either remains in the same state, or is kicked out forward, depending on the collision velocity and phase shift between the solitons. 相似文献
12.
Jun-Rong He 《Optics Communications》2011,284(12):3084-783
We present analytical bright multisoliton solutions to the generalized nonautonomous nonlinear Schrödinger equation with time- and space-dependent distributed coefficients in Fourier-synthesized optical lattice potential based on the similarity transformation technique. Such solutions exist in certain constraint conditions on the coefficients depicting dispersion, nonlinearity, and gain (or loss). Various shapes of bright solitons and interesting interactions between two solitons are observed, including soliton trains, collapse and revival of condensates, and two periodic M-shape solitons with collision. Phenomena of a few solitons and physical applications of interest to the field are discussed. 相似文献
13.
Solitons are generated in an anharmonic linear lattice in which neighbouring atoms interact through a Morse potential by giving either a strong initial impulse or a large displacement to an end atom. Studies on the variation of the characteristic properties of the soliton with the strength of the initial pulse show that the velocity and the amplitude of the soliton increase with the strength of the initial impulse, but below a certain critical value for the initial impulse, only an oscillatory tail is generated. It is shown that when a defect is present in the lattice, a localised mode appears at the site of the defect and additional solitons travelling forward or even backwards, are generated. When two solitons collide at a defect region, they reemerge but leave a localised mode at the site of the defect. If an initial velocity is imparted to a particular particle, synchronously with the crossing of the particle by the soliton, a localised mode emerges at the site of the particle and additional solitons are also generated. When a soliton moves from a denser to a rarer medium, a strong localised pulse is created near the region of the density discontinuity and additional solitons appear; and further a weak oscillatory tail is left behind in the denser medium. On the other hand, if a soliton moves from a rarer to a denser medium, it is reflected back and a small localised mode is generated at the site of the density discontinuity. The variation of amplitude of the soliton with the velocity of propagation is also studied. 相似文献
14.
Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential 下载免费PDF全文
This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrdinger 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. 相似文献
15.
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. 相似文献
16.
《Physics letters. A》2020,384(29):126761
A new (1+1)-dimensional integrable model is investigated, of which the Lax integrability is shown by the existence of its fifth order spectral problems. Its bilinear form is obtained via introducing an auxiliary variable. The multiple soliton solutions are obtained by solving its bilinear system. It is shown that there are four different dispersion relations for multiple solitons. The amplitudes of the solitons are only wave number dependent while the velocities of the solitons are not only wave number dependent but also dispersion relation dependent. Because of the existence of four dispersion relations, the interactions among solitons are much more abundant because for any fixed wave number there are four different velocities including two left moving and two right moving. Especially, the existence of the multiple velocities makes the velocity resonant conditions can be readily satisfied to form many types of bound states including soliton molecules, soliton-breather molecules and breather molecules. 相似文献
17.
M. R. Zhang X. Y. Jiang Y. L. Zhang L. Shi J. Zi J. Y. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(3):269-278
We systematically investigate slowly moving matter-wave gap
soliton propagation in weak random optical lattices. With the weak
randomness, an effective-particle theory is constructed to show
that the motion of a gap soliton is similar to a particle moving
in random potentials. Based on the effective-particle theory, the
effects of the randomness on gap solitons are obtained and the
trajectories of gap solitons are well predicted. Moreover, the
general laws that describe the movement depending on the weak
randomness are obtained. We find that with an increase of the
random strength, the ensemble-average velocity reduces slowly and
the reflection probability becomes larger. The theoretical results
based on the effective-particle theory are confirmed by the
numerical simulations based on the Gross-Pitaevskii equation. 相似文献
18.
19.
V. N. Likhachev T. Yu. Astakhova G. A. Vinogradov 《Russian Journal of Physical Chemistry B, Focus on Physics》2011,5(6):1023-1037
In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity
process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce
the time of computation of heat conductivity at ΔT → 0. The threshold temperature T
thr is found to behave as T
thr ∼ N
−3, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T
thr, phonon heat conductivity is dominant; at T > T
thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat
conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium
process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de
Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires
further study. 相似文献
20.
We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study
the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein
condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number
of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number
by a factor of √1 − bg
3 with g
3 the coupling constant of the lattice potential and b = 0.7301.
相似文献