共查询到20条相似文献,搜索用时 15 毫秒
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By developing a small amplitude soliton approximation method, we study analytically weak nonlinear excitations in cigar-shaped condensates with repulsive interatomic interaction under consideration of external perturbation potential. It is shown that matter wave solitons may exist and travel over a long distance without attenuation and change in shape by properly adjusting the strength of interatomic interaction to compensate for the effect of external perturbation potential. 相似文献
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A direct approach has been developed for soliton perturbations based on the Green's function. We first linearized the soliton equation, and then derived the Green's function corresponding to approximation equations of different orders. Finally, we obtained the effects of perturbation on a soliton, namely both the slow time dependence of the soliton parameters and the corrections up to the second-order approximation. The higher-order effects can also be obtained in the same way. 相似文献
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E. Arévalo Yu. Gaididei F.G. Mertens 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(1):63-74
We investigate the dynamics of a lattice soliton on a monatomic chain in the presence of damping and external forces. We consider
Stokes and hydrodynamical damping. In the quasi-continuum limit the discrete system leads to a damped and forced Boussinesq
equation. By using a multiple-scale perturbation expansion up to second order in the framework of the quasi-continuum approach
we derive a general expression for the first-order velocity correction which improves previous results. We compare the soliton
position and shape predicted by the theory with simulations carried out on the level of the monatomic chain system as well
as on the level of the quasi-continuum limit system. For this purpose we restrict ourselves to specific examples, namely potentials
with cubic and quartic anharmonicities as well as the truncated Morse potential, without taking into account external forces.
For both types of damping we find a good agreement with the numerical simulations both for the soliton position and for the
tail which appears at the rear of the soliton. Moreover we clarify why the quasi-continuum approximation is better in the
hydrodynamical damping case than in the Stokes damping case.
Received 22 August 2001 and Received in final form 7 December 2001 相似文献
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V. V. Tyutin 《Radiophysics and Quantum Electronics》1997,40(7):584-590
We found an envelope soliton solution of the third-order approximation equation of nonlinear wave dispersion theory (the so-called perturbed nonlinear Schrödinger equation) containing both nonlinear dispersion terms and a small linear aberration term. The solution was found by the perturbation technique with respect to the linear aberration parameter. 相似文献
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The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries (KdV) and nonlinear Schrödinger (NLS) equations. The rational solutions for the two equations has been obtained. The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations. The Sagdeev's potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation. The soliton and double layer solutions are obtained as a small amplitude approximation. A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed. 相似文献
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S. E. Harris 《Radiophysics and Quantum Electronics》1993,36(8):540-542
A mathematical model for gas-fluidized beds is examined which treats both the particles and gas as continua by volume averaging. The system is then considered as two interlocking one-phase fluids. For small perturbations to the uniform state, these equations have been shown by Crighton (1991) to reduce to the Burgers-KdV equation and under certain criteria, we have instability. We consider the unstable situation when the amplification effects are a perturbation to the KdV equation and take an initial condition of a single KdV soliton. The growth of this soliton is followed through several regions in which the unstable Burgers-KdV equation is no longer appropriate, but KdV remains the leading order equation. Eventually, there is a fundamental change in the solution and the new governing equations are fully nonlinear and O(1). These admit a solitary wave solution which matches back onto the KdV soliton. Thus, we can follow the formation of a bubble from a small amplitude perturbation to the uniform state.University of Cambridge, Cambridge, United Kingdom. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 797–800, August, 1993. 相似文献
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Asymmetric W-shaped and M-shaped soliton pulse generated from a weak modulation in an exponential dispersion decreasing fiber 下载免费PDF全文
We study localized waves on continuous wave background in an exponential dispersion decreasing fiber with two orthogonal polarization states. We demonstrate that asymmetric W-shaped and M-shaped soliton pulse can be generated from a weak modulation on continuous wave background. The numerical simulation results indicate that the generated asymmetric soliton pulses are robust against small noise or perturbation. In particular, the asymmetric degree of the asymmetric soliton pulse can be effectively controlled by changing the relative frequency of the two components. This character can be used to generate other nonlinear localized waves, such as dark–antidark and antidark–dark soliton pulse pair, symmetric W-shaped and M-shaped soliton pulse. Furthermore, we find that the asymmetric soliton pulse possesses an asymmetric discontinuous spectrum. 相似文献
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We study the propagation of (1+1)-dimensional spatial soliton in a
nonlocal Kerr-type medium with weak nonlocality. First, we show that
an equation for describing the soliton propagation in weak
nonlocality is a nonlinear Schr?dinger equation with
perturbation terms. Then, an approximate analytical solution of the
equation is found by the perturbation method. We also find some
interesting properties of the intensity profiles of the soliton. 相似文献
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H. -J. Mikeska B. Vaz da costa H. C. Fogedby 《Zeitschrift für Physik B Condensed Matter》1989,77(1):119-127
The effect of quantum fluctuations on solitons in the easy-plane ferromagnetic chain is considered within the semiclassical approximation. In accordance with the low temperature ideal gas picture we treat the solitons as a Boltzmann gas and impose quantisation on the spin wave spectrum. We present a method which allows to calculate quantum corrections in a systematic perturbation expansion in 1/S, whereS is the spin length. We use this method to obtain the soliton energy to second order at zero temperature. Our results indicate that the semiclassical approach reasonably describes quantum effects on soliton properties. 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(2):188-229
Abstract In the framework of a multidimensional superposition principle involving an analytical approach to nonlinear PDEs, a numerical technique for the analysis of soliton invariant manifolds is developed. This experimental methodology is based on the use of computer simulation data of soliton–perturbation interactions in a system under investigation, and it allows the determination of the dimensionality of similar manifolds and partially (in the small amplitude perturbation limit) to restore the related superposition formulae. Its application for cases of infinite dimensionality, and the question of approximation by lower dimensional manifolds and, respectively, by superposition formulae of a lower order are considered as well. The ideas and implementation details are illustrated and verified by using examples with the integrable, MKdV and KdV equations, and also nonintegrable, Kawahara and Regularized Long Waves equation, soliton models. 相似文献
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光折变介质中空间光孤子自弯曲现象研究 总被引:1,自引:0,他引:1
光折变非线性介质在外加直流电压时会引起介质内部电荷移动,而移动后的电荷又会导致空间电荷的扩散效应,从而产生非局域非线性现象。从理论上研究了具有流动和扩散非局域非线性的光折变晶体中所支持的空间光学孤子的传播行为。应用等效粒子近似方法分析了这类介质中(1 1)维空间光学孤子动力学行为,得出孤子运动"加速度"显式解。孤子的有效"加速度"决定于孤子参量和光折变非局域参量。所得的解析结果可在一定参量范围内直接用来计算孤子的传播轨迹。对孤子在光折变非局域非线性作用下的传播动力学行为做了仿真模拟,数值模拟结果与理论分析结论符合得很好。 相似文献
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We investigated the nonlinear Langmuir waves in a multi-ion-component low-temperature plasma. Beginning with the
fluid theory of plasma, and taking fully nonlinear response of the
low-frequency ion motion into account, we derived a set of equations governing the nonlinear coupling of the amplitude of the Langmuir wave and the low-frequency perturbation density. Using the Sagdeev potential method, we analyzed the characteristics of solitary wave. In the limit of small amplitude, the envelope soliton was found. Our investigation demonstrates
that the properties of soliton in a multi-ion-component plasma
are different from those of soliton in an electron-ion plasma. 相似文献
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By writing the perturbed Korteweg-de Vries equation (1) in operator form (2), we derive equations which are a basis for a perturbation method. In particular, in the first approximation, we obtain from them equations describing the evolution of the soliton amplitude and velocity. The present theory may be extended, also, to other nonlinear evolution equations if they are solved, without perturbation, by the inverse-problem method. 相似文献
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We study the nonlinear dynamics of a completely inhomogeneous DNA chain which is governed by a perturbed sine-Gordon equation. A multiple scale perturbation analysis provides perturbed kink-antikink solitons to represent open state configuration with small fluctuation. The perturbation due to inhomogeneities changes the velocity of the soliton. However, the width of the soliton remains constant. 相似文献
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We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross-Pitaevskii equation, trapped in a shallow optical-latticepotential. Based on the direct approach of perturbation theory for the nonlinear Schrödinger equation, we demonstrate that the height (as well as width) of bright soliton may have little change through selecting experimental parameters. 相似文献
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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. 相似文献