共查询到20条相似文献,搜索用时 62 毫秒
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The variational method is used to derive correlation equations that model phase jitter in dispersion-managed soliton systems. The predictions of these correlation equations are consistent with numerical solutions of the nonlinear Schr?dinger equation on which they are based. 相似文献
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We obtain exact spatiotemporal periodic traveling wave solutions to the generalized (3+1)-dimensional nonlinear Schr?dinger equation with distributed coefficients. We utilize these solutions to construct analytical light bullet soliton solutions of nonlinear optics. 相似文献
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Two-dimensional accessible solitary wave families of the
generalized nonlocal nonlinear Schr?dinger equation are obtained by
utilizing superpositions of various single accessible solitary solutions.
Specific values of soliton parameters are selected as initial conditions and
the superposition of known single solitary solutions in the highly nonlocal
regime are launched into the nonlocal nonlinear medium with a Gaussian
response function, to obtain novel numerical solitary solutions of improved
stability. Our results reveal that in nonlocal media with the Gaussian
response the higher-order spatial accessible solitary families can exist in
various forms, such as asymmetric necklace, asymmetric fractional, and
symmetric multipolar necklace solitons. 相似文献
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R. Fedele H. Schamel 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(3):313-320
An investigation to deepen the connection between the family of nonlinear Schr?dinger equations and the one of Korteweg-de
Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis
for the current velocity, it is proven that the cubic nonlinear Schr?dinger equation, whose solution is a complex wave function,
can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the
latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the
current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schr?dinger equation,
starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current
velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant
current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily
large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u0 with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined
variable x-u0 s (s being a time-like variable). This novel method in solving the nonlinear Schr?dinger equation starting from the Korteweg-de
Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the
present paper and the ones already known in literature is also presented.
Received 20 February 2002 and Received in final form 22 April 2002 Published online 6 June 2002 相似文献
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Palacios SL Guinea A Fernández-Díaz JM Crespo RD 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,60(1):R45-R47
We solve the higher order nonlinear Schr?dinger equation describing the propagation of ultrashort pulses in optical fibers. By means of the coupled amplitude-phase formulation fundamental (solitary wave) dark soliton solutions are found. 相似文献
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Bound-State Soliton Solutions of the Nonlinear Schr?dinger Equation and Their Asymmetric Decompositions
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We study the asymmetric decompositions of bound-state(BS) soliton solutions to the nonlinear Schr?dinger equation. Assuming that the BS solitons are split into multiple solitons with different displacements, we obtain more accurate decompositions compared to the symmetric decompositions. Through graphical techniques, the asymmetric decompositions are shown to overlap very well with the real trajectories of the BS soliton solutions. 相似文献
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I. Goidenko I. Tupitsyn G. Plunien 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,45(1):171-177
In this paper, we present a family of coupled higher-order
nonlinear Schr?dinger equation describing the optical soliton pulse
propagating in inhomogeneous optical fiber media. The exact N-soliton
solution and its characteristics of stabilities and novel elastic collision
properties are studied in detail. As an example, we give the relative
numerical evolutions by a soliton control system to discuss the pulses
propagation characteristics. 相似文献
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Symmetric and Anti-Symmetric Solitons of the Fractional Second-and Third-Order Nonlinear Schr?dinger Equation
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《中国物理快报》2021,(9)
The fractional second-and third-order nonlinear Schr?dinger equation is studied,symmetric and antisymmetric soliton solutions are derived,and the influence of the Levy index on different solitons is analyzed.The stability and stability interval of solitons are discussed.The anti-interference ability of stable solitons to the small disturbance shows a good robustness. 相似文献
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We construct the soliton solution and smooth positon solution of the second-type derivative nonlinear Schr¨odinger(DNLSII) equation. Additionally, we present a detailed discussion about the decomposition of the positon solution, and display its approximate orbits and variable "phase shift". The second and third order breather-positon solutions are also constructed. 相似文献
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B. Saka 《Physics of Wave Phenomena》2012,20(2):107-117
The nonlinear Schr?dinger equation is numerically solved using the collocation method based on quintic B-spline interpolation functions. The efficiency and robustness of the proposed method are demonstrated by standard test problems, such as a one-soliton solution, interaction of two solitons, and formation of a soliton. This method is compared with both the analytical and numerical techniques in the computational section. 相似文献
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利用分离变量法,研究了(2+1)维非线性薛定谔(NLS)方程的局域结构.由于在B?cklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了NLS方程丰富的局域结构.合适地选择任意函数,局域解可以是dromion,环孤子,呼吸子和瞬子.dromion解不仅可以存在于直线孤子的交叉点上,也可以存在于曲线孤子的最近邻点上.呼吸子在幅度和形状上都进行了呼吸
关键词:
非线性薛定谔方程
分离变量法
孤子结构 相似文献
18.
The Jacobian elliptic function expansion method for nonlinear
differential-different equations and its algorithm are presented
by using some relations among ten Jacobian elliptic functions and
successfully construct more new exact doubly-periodic solutions of
the integrable discrete nonlinear Schr ödinger equation. When the
modulous m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark
soliton, new solitons as well as trigonometric function solutions. 相似文献
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Observation of temporal vector soliton propagation and collision in birefringent fiber 总被引:1,自引:0,他引:1
Rand D Glesk I Brès CS Nolan DA Chen X Koh J Fleischer JW Steiglitz K Prucnal PR 《Physical review letters》2007,98(5):053902
We report the experimental observation of temporal vector soliton propagation and collision in a linearly birefringent optical fiber. To the best of the authors' knowledge, this is both the first demonstration of temporal vector solitons with two mutually incoherent component fields, and of vector soliton collisions in a Kerr nonlinear medium. Collisions are characterized by an intensity redistribution between the two components, and the experimental results agree with numerical predictions of the coupled nonlinear Schr?dinger equation. 相似文献
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Yang J 《Physical review letters》2003,91(14):143903
Stable embedded solitons are discovered in the generalized third-order nonlinear Schr?dinger equation. When this equation can be reduced to a perturbed complex modified Korteweg-de Vries equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum. 相似文献