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W. P.?Zhong M.?Beli? R. H.?Xie G.?Chen Y. Q.?Lu 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,55(1):147-153
Bright and dark matter wave solitons are
constructed analytically in a three-dimensional (3D) highly anisotropic
Bose-Einstein condensate (BEC) with a time-dependent parabolic potential,
and numerical simulations are performed to confirm the existence and
dynamics of such analytical solutions. Different classes of bright and dark
solitons are discovered among the solutions of the generalized anisotropic
(3+1)D Gross-Pitaevskii equation. Our results demonstrate that the bright
and dark solitary waves can be manipulated and controlled by changing the
scattering length, which can be used to compress the second-order bright and
dark solitons of BECs into desired peak density. 相似文献
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Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a harmonic potential, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. A particle analogy for the solitary waves is formulated and shown to be integrable for a two-particle system. The extension to three particles is shown to support chaotic regimes. Good agreement is found between the particle model and simulations of the full wave dynamics, suggesting that the dynamics can be described in terms of solitons both in regular and chaotic regimes, presenting a paradigm for chaos in wave mechanics. 相似文献
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Using a three-dimensional mean-field model we study one-dimensional dipolar Bose–Einstein condensate (BEC) solitons on a weak two-dimensional (2D) square and triangular optical lattice (OL) potentials placed perpendicular to the polarization direction. The stabilization against collapse and expansion of these solitons for a fixed dipolar interaction and a fixed number of atoms is possible for short-range atomic interaction lying between two critical limits. The solitons collapse below the lower limit and escapes to infinity above the upper limit. One can also stabilize identical tiny BEC solitons arranged on the 2D square OL sites forming a stable 2D array of interacting droplets when the OL sites are filled with a filling factor of 1/2 or less. Such an array is unstable when the filling factor is made more than 1/2 by occupying two adjacent sites of OL. These stable 2D arrays of dipolar superfluid BEC solitons are quite similar to the recently studied dipolar Mott insulator states on 2D lattice in the Bose–Hubbard model by Capogrosso-Sansone et al. [B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo, Phys. Rev. Lett. 104 (2010) 125301]. 相似文献
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S. Komineas 《The European physical journal. Special topics》2007,147(1):133-152
We discuss nonlinear excitations in an atomic Bose–Einstein condensate which is trapped in a harmonic potential. We focus
on axially symmetric solitary waves propagating along a cylindrical condensate. A quasi one-dimensional dark soliton is the
only nonlinear mode for a condensate with weak interactions. For sufficiently strong interactions of experimental interest
solitary waves are hybrids of one-dimensional dark solitons and three-dimensional vortex rings. The energy-momentum dispersion
of these solitary waves exhibits
characteristics similar to a mode proposed sometime ago by Lieb
in a strictly 1D model, as well as some rotonlike features.
We subsequently discuss interactions between solitary waves.
Head-on collisions between dark solitons are elastic.
Slow vortex rings collide elastically but faster ones
form intermediate structures during collisions before they lose
energy to the background fluid.
Solitary waves and their interactions have been observed in experiments.
However, some of their intriguing features still remain to be
experimentally identified. 相似文献
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以描述负折射介质中超短脉冲传输的归一化非线性薛定谔方程为模型,采用对称分步傅里叶算法研究了负折射介质中亮、暗孤波间的相互作用.数值模拟发现:当孤波的初始频移为零时,亮孤波间的相互作用与常规介质中类似;当孤波的初始频移不为零时,其传输速度和相互作用明显受三阶色散和自陡峭效应的影响,主要表现为相互排斥.而负折射介质中暗孤波间的相互作用与常规介质中的相互作用类似,无论暗孤波是否存在初始频移,暗孤波间的相互作用在三阶色散和自陡峭的影响下都表现为相互排斥.结果表明,通过调节三阶色散和自陡峭系数可以在一定程度上抑制负折射介质中亮、暗孤波间的相互作用.该研究结果为负折射介质在未来高速通信中的应用提供了理论依据. 相似文献
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以描述负折射介质中超短脉冲传输的归一化非线性薛定谔方程为模型,采用对称分步傅里叶算法研究了负折射介质中亮、暗孤波间的相互作用.数值模拟发现:当孤波的初始频移为零时,亮孤波间的相互作用与常规介质中类似;当孤波的初始频移不为零时,其传输速度和相互作用明显受三阶色散和自陡峭效应的影响,主要表现为相互排斥.而负折射介质中暗孤波间的相互作用与常规介质中的相互作用类似,无论暗孤波是否存在初始频移,暗孤波间的相互作用在三阶色散和自陡峭的影响下都表现为相互排斥.结果表明,通过调节三阶色散和自陡峭系数可以在一定程度上抑制负折射介质中亮、暗孤波间的相互作用.该研究结果为负折射介质在未来高速通信中的应用提供了理论依据. 相似文献
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We investigate the exact bright and dark solitary wave solutions of an effective 1D Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. (2004) [50], Serkin et al. (2007) [51], Gurses (2007) [52] and Kundu (2009) [53], we point out that the effective 1D equation resulting from the Gross-Pitaevskii (GP) equation can be transformed into the standard soliton (bright/dark) possessing, completely integrable 1D nonlinear Schrödinger (NLS) equation by effecting a change of variables of the coordinates and the wave function. We consider both confining and expulsive harmonic trap potentials separately and treat the atomic scattering length, gain/loss term and trap frequency as the experimental control parameters by modulating them as a function of time. In the case when the trap frequency is kept constant, we show the existence of different kinds of soliton solutions, such as the periodic oscillating solitons, collapse and revival of condensate, snake-like solitons, stable solitons, soliton growth and decay and formation of two-soliton bound state, as the atomic scattering length and gain/loss term are varied. However, when the trap frequency is also modulated, we show the phenomena of collapse and revival of two-soliton like bound state formation of the condensate for double modulated periodic potential and bright and dark solitons for step-wise modulated potentials. 相似文献
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In this letter the three-dimensional nonlinear Helmholtz equation is investigated, which describes electro-magnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic functionsolutions are obtained, by using our extended Jacobian elliptic function expansion method. When the modulus m → 1or0, the corresponding solitary waves including bright solitons, dark solitons and new line solitons and singly periodicsolutions can be also found. 相似文献
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YANGYong YANZhen-Ya 《理论物理通讯》2002,38(6):657-659
In this letter the three-dimensional nonlinear Helmholtz equation is investigated.which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained,by using our extended Jacobian elliptic function expansion method.When the modulus m-→1 or 0,the corresponding solitary waves including bright solitons,dark solitons and new line solitons and singly periodic solutions can be also found. 相似文献
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Merging and splitting dynamics between two bright solitons in dipolar Bose-Einstein condensates
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We numerically study the interaction dynamics of two bright solitons with zero initial velocities in the one-dimensional dipolar Bose-Einstein condensates. Under different dipolar strengths, the two bright solitons can merge into a breathing wave, and then split or propagate constantly after several oscillating periods. We quantitatively study the breathing frequency of wave after merging and the asymmetry property of solitons after splitting, and analyze their formation mechanism by the system's energy evolution. Also, the change of initial phase difference brings distinct effects on the soliton interaction. Our results provide insight into the new dynamical phenomena in dipolar systems and enrich the understanding for interaction between dipolar solitons. 相似文献
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《Physics letters. A》2020,384(27):126729
The integrability nature of a nonparaxial nonlinear Schrödinger (NNLS) equation, describing the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied by employing the Painlevé singularity structure analysis. Our study shows that the NNLS equation fails to satisfy the Painlevé test. Nevertheless, we construct one bright solitary wave solution for the NNLS equation by using the Hirota's direct method. Also, we numerically demonstrate the stable propagation of the obtained bright solitary waves even in the presence of an external perturbation in a form of white noise. We then numerically investigate the coherent interaction dynamics of two and three bright solitary waves. Our study reveals interesting energy switching among the colliding solitary waves due to the nonparaxiality. 相似文献
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Sasanka Ghosh 《Pramana》2001,57(5-6):981-985
Existence of a new class of complex solitary waves is shown for Sasa Satsuma equation. These solitary waves are found to be
stable in a certain domain of the parameter and become chaotic if the parameter exceeds the value 2.4. Significantly, the
complex solitary waves propagate at higher bit rate over the most stable solitons under the same conditions of the input parameters. 相似文献
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We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks. 相似文献
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We study (2+1) -dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents and demonstrate that these solitary waves exhibit a symmetry-breaking instability, provided their total topological charge is nonzero. We describe a novel type of stable multicomponent dipole-mode solitons with intriguing swinging dynamics. 相似文献
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The methodology developed provides for a systematic way to find an infinite number of the novel stable bright and dark "soliton islands" in a "sea of solitary waves" of the nonlinear Schrodinger equation model with varying dispersion, nonlinearity, and gain or absorption. It is shown that solitons exist only under certain conditions and the parameter functions describing dispersion, nonlinearity, and gain or absorption inhomogeneities cannot be chosen independently. Fundamental soliton management regimes are discovered. 相似文献
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Exact analytical solutions for pulse propagation in a nonlinear coupled cubic–quintic complex Ginzburg–Landau equations are obtained. Three families of solitary waves which describe the evolutions of progressive bright–bright, front–front, dark–dark and other families of solitary waves are investigated. These exact solutions are analyzed both for competition of loss or gain due to nonlinearity and linearity of the system. The stability of the solitary waves is examined using analytical and numerical methods. The results reveal that the solitary waves obtained here can propagate in a stable way under slight perturbation of white noise and the disturbance of parameters of the system. 相似文献