共查询到20条相似文献,搜索用时 656 毫秒
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映射法是一种非常经典、有效和成熟的求解非线性演化方程的方法,其最大的特点是可以有多种不同形式的设解,使得最终求得的解丰富多彩. 利用改进的 Riccati 方程映射法和变量分离法,得到了(2+1)维非对称 Nizhnik-Novikov-Veselov 系统的新显式精确解.根据得到的孤波解,构造出该系统的峰孤子和分形孤子等局域结构,研究了两个孤立波的“追碰”现象.
关键词:
改进的映射法
(2+1)维非对称 Nizhnik-Novikov-Veselov 系统
局域结构
“追碰”现象 相似文献
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By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek--Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated. 相似文献
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MA Song-Hua QIANG Ji-Ye FANG Jian-Ping 《理论物理通讯》2007,48(4):662-666
By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions) to the (2+1)-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note. 相似文献
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The properties of dust-ion-acoustic (DIA) solitons in an unmagnetized dusty plasma, whose constituents are adiabatic ion-fluid,
Boltzmann electrons, and static dust particles, are investigated by employing the reductive perturbation method. The Korteweg-de
Vries equation is derived and its stationary solution is numerically analyzed. The parametric regimes for the existence of
positive and negative solitons are found. It has been shown that ion-fluid temperature not only significantly modifies the
basic features (width and amplitude) of DIA solitons, but also introduces some new features of DIA solitons.
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The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied.The interaction between bright solitons in different species with small separation is derived.Unlike the interaction between solitons of the same species,it is independent of the phase difference between solitons.It may be of attraction or repulsion.In the former case,each soliton will oscillate about and pass through each other around the mass-center of the system,which will also oscillate harmonically due to the harmonic trapping potential. 相似文献
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We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex
solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media. 相似文献
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一维光伏空间灰孤子及其稳定性研究 总被引:4,自引:2,他引:2
从考虑背景光的光伏作用后的光束在光伏媒质中传播的方程出发,证明了在折射率改变为正的光伏媒质中也可以形成灰孤子。光束以灰孤子状态在光伏晶体中传播时,其横向相位必须具有一个与光强分布有关的形式分布,表达式为φ(s)=v[η-∫y^-2(η)dη],其中v是灰孤子的横向运动速度,η是无量纲化坐标,y(η)是归一化的光场振幅。分别讨论了光束灰度、光强振幅、信号光与背景光的有效Glass系数之比R对一维的光伏空间灰孤子宽度、横向总相移和横向运动速度的影响,并分析了光伏灰孤子的稳定性。当光束的灰度m为0时,这一理论可直接退化为光伏暗孤子的理论。 相似文献
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Dumitru Mihalache 《Central European Journal of Physics》2008,6(3):582-587
A brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic
analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative
solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary
solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on
computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity
in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental
(zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear
gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic
pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane.
Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland 相似文献
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Hongcheng Wang 《Frontiers of Physics》2016,11(5):114204
This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity–time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μ c for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ > μ c . In the self-defocusing case, solitons exist only when μ < μ c . Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects. 相似文献