共查询到20条相似文献,搜索用时 140 毫秒
1.
引进一类广义色散Camassa-Holm模型,对其做奇异性分析.通过改进的WTC-Kruskal算法,证明该模型在Painlevé意义下可积,得到了它的一组Painlevé-Bcklund系统和Bcklund变换.应用Maple进行代数运算,得到了丰富的规则(regular)孤子和一类奇异(singular)孤子,扭结(kink)孤子,紧孤子(compacton)和反紧孤子(anti-compacton).特别地,推导出一类在扭结孤子的中间区域包含有一列周期尖点(cuspon)波的奇异结构.在这些规则的孤子系统的基础上,对可积广义系统应用Bcklund变换,得到三类奇异孤子,分别是具有驼峰结构的周期爆破波,具有爆破波结构的扭结孤子和紧孤子.
关键词:
广义Camassa-Holm 模型
周期尖点波
紧孤子
周期爆破波 相似文献
2.
3.
采用双曲函数展开法得到Modified Benjamin-Bona-Mahony(mBBM)方程的一类扭结-反扭结状的双扭结孤立波解,在不同的极限情况下,此孤立波分别退化为mBBM方程的扭结状和钟状孤立波解.对双扭结型单孤子的结构特征进行分析,构造有限差分格式对其动力学稳定性进行数值研究.有限差分格式为两层隐式格式,在线性化意义下无条件稳定.数值结果表明mBBM方程的双扭结型单孤子在不同类型的扰动下均具有很强的稳定性.对双孤立波的碰撞进行数值模拟,发现既存在弹性碰撞也存在非弹性碰撞. 相似文献
4.
5.
数值研究了具有三体相互作用的均匀介质界面和半无限雅克比椭圆正弦势下准一维玻色-爱因斯坦凝聚体(Bose-Einstein condensate,BEC)中的表面带隙孤子及其稳定性.在平均场近似下,其动力学行为可用3次-5次Gross-Pitaevskii方程描述.首先用牛顿-共轭梯度法寻找表面带隙孤子,发现表面亮孤子仅当化学势小于0时才可于带隙内激发,但表面扭结孤子和气泡孤子既可存在于带隙中也可存在于能带中.然后采用线性稳定性分析和非线性动力学演化研究了孤子的稳定性,结果表明三体相互作用会明显影响表面亮孤子的稳定性,表面扭结孤子既有稳定的也有不稳定的,但表面气泡孤子均不稳定. 相似文献
6.
7.
8.
9.
利用扩展的双曲函数法得到了combined KdV-mKdV (cKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为cKdV方程的扭结状或钟状孤波解.理论分析表明,cKdV方程既有传播型孤立波解,也有非传播型孤立波解.文中对双扭结型孤立波解的稳定性进行了数值研究,结果表明,cKdV方程既存在稳定的双扭结型孤立波,也存在不稳定的双扭结型孤立波.
关键词:
cKdV方程
双扭结单孤子
稳定性 相似文献
10.
11.
《Physica D: Nonlinear Phenomena》2002,161(1-2):79-101
We investigate the interface coupling between the two-dimensional sine-Gordon equation and the two-dimensional wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effective one-dimensional model, and using soliton perturbation theory, compute the fixed points that can trap either a kink or antikink at an interface between two sine-Gordon media. This approximate analysis is validated by comparing with the solution of the partial differential equation and describes kink motion in the one-dimensional window junction. Using this, we analyze steady-state kink motion and derive values for the average speed in the one- and two-dimensional systems. Finally, we show how geometry and the coupling parameters can destabilize kink motion. 相似文献
12.
13.
In this paper, we study sine-Gordon equation in order to obtain exact solitary wave solutions in the domain of fractional calculus. By using the definition of conformable fractional derivative, we obtain analytical solutions of time, space and time-space fractional sine-Gordon equations. We analyze graphically the effect of fractional order on evolution of the kink and antikink type solitons. 相似文献
14.
We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory. 相似文献
15.
Gani VA Kudryavtsev AE 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,60(3):3305-3309
We studied the kink-antikink collision process for the "double sine-Gordon" (DSG) equation in 1+1 dimensions at different values of the potential parameter R>0. For small values of R we discuss the problem of resonance frequencies. We give qualitative explanation of the frequency shift in comparison with the frequency of the discrete level in the potential well of isolated kink. We show that in this region of the parameter R the effective long-range interaction between kink and antikink takes place. 相似文献
16.
T. Yanagisawa Y. Tanaka I. Hase K. Yamaji 《Physica C: Superconductivity and its Applications》2011,471(21-22):675-678
We investigate multi-component superconductors, in relation to iron pnictides, by using the Ginzburg–Landau theory. We show that a three-band superconductor exhibits several significant properties that are not found in single-band or two-band superconductors. The frustrating pairing interaction among Fermi surfaces may lead to a time-reversal symmetry broken pairing state. In fact, we have a solution with time-reversal symmetry breaking, that is, a chiral solution when there is such a frustration. The Ginzburg–Landau equation for three-component superconductors leads to a double sine-Gordon equation. A kink solution exists to this equation that results in the existence of fractional-quantum flux vortices on the domain wall. 相似文献
17.
Within the formalism of the Fokker-Planck equation, the influence of nonstationary external force, random force, and dissipation
effects on the kink dynamics is investigated in the sine-Gordon model. The equation of evolution of the kink momentum is obtained
in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin
and Scott energy approach. The corresponding Fokker-Planck equation for the momentum distribution function coincides with
the equation describing the Ornstein-Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear
stochastic effects on the kink dynamics is considered with the help of the Fokker-Planck nonlinear equation with the shift
coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average
value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random
forces on the evolution of the average value and variance of the kink momentum.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–51, February, 2008. 相似文献
18.
N.R. Quintero A. Sánchez F.G. Mertens 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(1):107-115
We study analytically and numerically the action of a constant force on the propagation of kinks in the φ4 and sine-Gordon systems, with and without dissipation. We specifically investigate the relation of the external force with
the oscillations of the kink width due to excitation of its internal mode or quasimode. We demonstrate that both dc force
and dissipation, either jointly or separately, damp the oscillations of the kink width. We further prove that, in contrast
to earlier predictions, those oscillations can only arise if we use a distorted kink as initial condition for the evolution.
Finally, we show that for the φ4 system the oscillations of the kink width come from the excitation of its internal mode, whereas in the sG equation they
originate in the excitation of the lowest radiational modes and an internal mode induced by the discreteness of the numerical
simulations.
Received 6 June 2000 相似文献
19.
N.R. Quintero A. Sánchez F.G. Mertens 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(2):361-368
We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the
correlation function of the position of the kink center as well as the diffusion coefficient, both up to second-order in temperature.
We find that the kink behavior is very similar to that obtained in the overdamped limit: There is a quadratic dependence on
temperature in the diffusion coefficient that comes from the interaction among the kink and phonons, and the average value
of the wave function increases with due to the variance of the centers of individual realizations and not due to kink distortions. These analytical results are
fully confirmed by numerical simulations.
Received 4 October 1999 and Received in final form 3 February 2000 相似文献
20.
We present numerical and analytic solutions to the perturbed sine-Gordon equation, which models long Josephson tunnel junctions. We make comparisons between numerical results and results obtained from perturbational methods. We present unstable, analytic kink solutions to the equation and further a solution, which is an array of kinks, corresponding to a solution, where the current through the junction is larger than the critical current. 相似文献