共查询到20条相似文献,搜索用时 519 毫秒
1.
Zhi-Yuan Sun Yi-Tian Gao Xiang-Hua Meng Xin Yu Ying Liu 《International Journal of Theoretical Physics》2013,52(3):689-698
Dark bound solitons and soliton chains without interactions are investigated for the higher-order nonlinear Schrödinger (HNLS) equation, which can model the propagation of the femtosecond optical pulse under some physical situations in nonlinear fiber optics. Via the modulation of parameters for the analytic solutions, different types of dark bound solitons and soliton chains can be derived for the HNLS equation. In addition, stabilities of those structures are checked through numerical simulations. Our discussions are expected to be helpful in interpreting those new structures, and applied to the long-distance transmission of the femtosecond pulses in optical fibers. 相似文献
2.
Luis A. Cisneros-Ake Hugo Parra Prado Diego Joselito López Villatoro R. Carretero-González 《Physics letters. A》2018,382(12):837-845
We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg–de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS–mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution. 相似文献
3.
Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation 下载免费PDF全文
Xuefeng Zhang 《中国物理 B》2023,32(1):10505-010505
We make a quantitative study on the soliton interactions in the nonlinear Schrödinger equation (NLSE) and its variable-coefficient (vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities (especially the soliton accelerations and interaction forces); whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles, particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics. 相似文献
4.
We investigate the nonlinear tunneling of optical solitons through both dispersion and nonlinear barriers by employing the exact solution of the generalized nonlinear Schrödinger equation with variable coefficients. The extensive numerical simulations show that the optical solitons can be efficiently compressed when they pass through adequate engineered nonlinear barriers. A cascade compression system in a dispersion decreasing fiber with nonlinear barriers on an exponential background is proposed and the cascade compression of optical pulses is further investigated in detail. Finally, the stability to various initial perturbations of the cascade compressed optical soliton and the interaction between two neighboring compressed solitons were investigated too. 相似文献
5.
由于变系数非线性Schrödinger方程的增益、色散和非线性项都是变化的, 根据方程这一特点可以研究光脉冲在非均匀光纤中的传输特性. 本文利用Hirota方法, 得到非线性Schrödinger方程的解析暗孤子解. 然后根据暗孤子解对暗孤子的传输特性进行讨论, 并且分析各个物理参量对暗孤子传输的影响. 经研究发现, 通过调节光纤的损耗、色散和非线性效应都能有效的控制暗孤子的传输, 从而提高非均匀光纤中的光脉冲传输质量. 此外, 本文还得到了所求解方程的解析双暗孤子解, 最后对两个暗孤子相互作用进行了探讨. 本文得到的结论有利于研究非均匀光纤中的孤子控制技术. 相似文献
6.
A. V. Slyunyaev E. N. Pelinovski 《Journal of Experimental and Theoretical Physics》1999,89(1):173-181
The interaction and generation of solitons in nonlinear integrable systems which allow the existence of a soliton of limiting
amplitude are considered. The integrable system considered is the Gardner equation, which includes the Korteweg-de Vries equation
(for quadratic nonlinearity) and the modified Korteweg-de Vries equation (for cubic nonlinearity) as special cases. A two-soliton
solution of the Gardner equation is derived, and a criterion, which distinguishes between different scenarios for the interaction
of two solitons, is determined. The evolution of an initial pulsed disturbance is considered. It is shown, in particular,
that solitons of opposite polarity appear during such evolution on the crest of a limiting soliton.
Zh. éksp. Teor. Fiz. 116, 318–335 (July 1999) 相似文献
7.
In this paper, we consider the nonlinear Schrödinger equation with variable coefficients, and by using direct transformation of variables and functions, the explicit chirped gray one- and two-soliton solutions are presented. Based on the exact solutions, we in detail analyze the propagation characteristics of the chirped gray soliton, including the stability against either the deviation from integrable condition or the initial perturbation, and interaction between the chirped gray solitons. The results show that the gray soliton can be compressed by choosing the appropriate initial chirp, and the chirped gray pulses can stably propagate along optical fibers remaining the character of solitons. 相似文献
8.
The coherent interaction scenarios of two solitons, three solitons, and four solitons are presented. For two-soliton interactions, energy transfer and fusion between solitons are dependent on the relative phase of the interaction solitons, and for multi-soliton interactions, energy transfer will occur in all three relative phase conditions. The magnitude and direction of energy transfer can be controlled respectively by adjusting the interval and the relative phase of solitons. 相似文献
9.
Higher-Dimensional KdV Equations and Their Soliton Solutions 总被引:2,自引:0,他引:2
A (2+1)-dimensional KdV equation is obtained by use of Hirota
method, which possesses N-soliton solution, specially its exact
two-soliton solution is presented. By employing a proper algebraic
transformation and the Riccati equation, a type of bell-shape
soliton solutions are produced via regarding the variable in the
Riccati equation as the independent variable. Finally, we extend
the above (2+1)-dimensional KdV equation into (3+1)-dimensional
equation, the two-soliton solutions are given. 相似文献
10.
11.
Based on a special transformation that we introduce, the N-soliton solution of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is constructed. By applying the long wave limit and restricting certain conjugation conditions to the related solitons, some novel localized wave solutions are obtained, which contain higher-order breathers and lumps as well as their interactions. In particular, by choosing appropriate parameters involved in the N-solitons, two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution. Five solutions including two breathers, two lumps, and interaction solutions between one breather and two bell-shaped solitons, one breather and one lump, or one lump and two bell-shaped solitons are constructed from the 4-soliton solution. Five interaction solutions mixed by one breather/lump and three bell-shaped solitons, two breathers/lumps and a bell-shaped soliton, as well as mixing with one lump, one breather and a bell-shaped soliton are constructed from the 5-soliton solution. To study the behaviors that the obtained interaction solutions may have, we present some illustrative numerical simulations, which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties. The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations. The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations. 相似文献
12.
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
13.
基于包含五次复系数的高阶Ginzburg Landau方程为模型,采用分步傅里叶方法数值研究了啁啾类超短脉冲间的相互作用。结果表明:相邻孤子之间的相互作用对五阶非线性效应非常敏感,即使参数改变很小的值,也会改变其传输特性。适当地选择五阶非线性参数值,能够很好地抑制孤子间的相互作用,提高光纤传输的比特率。当相邻孤子的初始间距为6.8,五阶非线性参数值取-0.001时,可以实现2个孤子长距离的保型传输。最后讨论了五阶非线性作用下多孤子之间的相互作用及抑制。 相似文献
14.
Considering the ultrashort optical soliton propagation in the non-Kerr media, the cubic-quintic nonlinear Schrödinger equation with Raman effect is studied through the dependent variable transformation and Hirota method. Based on symbolic computation, the bilinear form, the explicit one- and two-soliton solutions for the equation are presented. The constraint parametric condition for the existence of soliton solutions is also derived. Propagation characteristics and interaction behaviors of the solitons are graphically shown and discussed: (1) Overtaking elastic interactions of the two solitons; (2) periodic attraction and repulsion of the bounded states of two solitons; (3) propagation in parallel of the two solitons. 相似文献
15.
In this paper, we obtain a new class of exact cross kink-wave and periodic solitary-wave solutions for Jimbo-Miwa equation by using two-soliton method, bilinear method and transforming parameters into complex ones. Moreover, we investigate singular and non-singular phenomenons of solutions. In addition, we study the resonance and non-resonance interactions between y-t periodic solitons and different line solitons. 相似文献
16.
We present new types of solitary wave solutions for the higher order nonlinear Schrodinger (HNLS) equation describing propagation of femtosecond light pulses in an optical fiber under certain parametric conditions. Unlike the reported solitary wave solutions of the HNLS equation, the novel ones can describe bright and dark solitary wave properties in the same expressions and their amplitude may approach nonzero when the time variable approaches infinity. In addition, such solutions cannot exist in the nonlinear Schrodinger equation. Furthermore, we investigate the stability of these solitary waves under some initial pertubations by employing the numerical simulation methods. 相似文献
17.
In this paper, we present exact femtosecond one- and two-dark soliton solutions for a variable-coefficient higher-order nonlinear Schrödinger equation via modified Hirota method. The propagation and interaction of femtosecond dark solitons are investigated in inhomogeneous fiber systems. Elastic collision, bound oscillation and parallel propagation can be achieved in both Gaussian distributed parameter system and exponentially periodic distributed parameter system by choosing the appropriate distributed parameters and soliton parameters. The results may be beneficial to the realization of interaction control of femtosecond dark solitons in communication systems. 相似文献
18.
Soliton interaction and control using the dispersion-decreasing fibers with potential applications to the design of high-speed optical devices and ultralarge capacity transmission systems are investigated based on solving the variable-coefficient nonlinear Schr?dinger equation with symbolic computation. Via the Hirota method, analytic two- and three-soliton solutions for that model are obtained, with their relevant properties and features illustrated. Dispersion-decreasing fibers with different profiles are found to be able to control the soliton velocity. Additionally, through the asymptotic analysis for the two-soliton solutions, we point out that the interaction between two solitons is elastic. Finally, a new approach to controll the soliton interaction using the dispersion-decreasing fiber with the Gaussian profile is suggested. 相似文献
19.
For two-component disk-shaped Bose-Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a
Kadomtsev-Petviashvili-I equation at the lowest order from the original coupled Gross-Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev-Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as
well. The instability of a soliton under higher-order long
wavelength disturbance has been investigated. It is found that the
instability depends on the angle between two directions of both
soliton and disturbance. 相似文献
20.
A certain critical two-soliton solution of the nonlinear Schroedinger equation 总被引:1,自引:0,他引:1 下载免费PDF全文
An exact two-soliton solution of the nonlinear Schroedinger equation is derived by using the Hirota direct approach. This solution describes such a critical process that two still solitons separated infinitely approach and then pass through each other and keep straight on infinitely. 相似文献