共查询到20条相似文献,搜索用时 15 毫秒
1.
单摆链上的孤子波演示 总被引:2,自引:2,他引:0
从扭转弹性棒上的单摆链导出了SineGordon方程,该方程有孤子解.用橡皮筋和大头针制成的简单单摆链机械系统,可演示SineGordon方程的孤子波. 相似文献
2.
Toshiaki Kaminaka Miki Wadati 《Physics letters. A》2011,375(24):2460-2464
We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum. 相似文献
3.
P. Surya Mohan Tanja Tarvainen Martin Schweiger Aki Pulkkinen Simon R. Arridge 《Journal of computational physics》2011,230(19):7364-7383
We propose the PN approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the PN approximation is compared against Monte Carlo simulations and other state-of-the-art methods. 相似文献
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In this paper, we studied N-soliton solutions of a new integrable equation studied by Qiao [J. Math. Phys. 48 082701 (2007)]. Firstly, we employed the Darboux matrix method to construct a Darboux transformation for the modified Korteweg-de Vries equation. Then we use the Darboux transformation and a transformation, introduced by Sakovich [J. Math. Phys. 52 023509 (2011)], to derive N-soliton solutions of the new integrable equation from the seed solution. In particular, the multiple soliton solutions are explicitly obtained and shown through some figures. 相似文献
6.
The nonlocal nonlinear Gerdjikov-Ivanov (GI) equation is one of the most important integrable equations, which can be reduced from the third generic deformation of the derivative nonlinear Schrödinger equation. The Darboux transformation is a successful method in solving many nonlocal equations with the help of symbolic computation. As applications, we obtain the bright-dark soliton, breather, rogue wave, kink, W-shaped soliton and periodic solutions of the nonlocal GI equation by constructing its 2n-fold Darboux transformation. These solutions show rich wave structures for selections of different parameters. In all these instances we practically show that these solutions have different properties than the ones for local case. 相似文献
7.
Wen-Xiu Ma 《理论物理通讯》2021,73(6):65001
A linear superposition is studied for Wronskian rational solutions to the Kd V equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions. 相似文献
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The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics 下载免费PDF全文
Using the projective Riccati equation expansion (PREE) method, new
families of variable separation solutions (including solitary wave
solutions, periodic wave solutions and rational function solutions)
with arbitrary functions for two nonlinear physical models are
obtained. Based on one of the variable separation solutions and by
choosing appropriate functions, new types of interactions between
the multi-valued and single-valued solitons, such as a peakon-like
semi-foldon and a peakon, a compacton-like semi-foldon and a
compacton, are investigated. 相似文献
10.
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
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采用行波法约化方程,建立一种变换关系,把求解(3+1)维NizhnikNovikovVeselov(NNV)方程的解转化为求解一维非线性KleinGordon方程的解,从而得到了(3+1)维NNV方程的孤子解和周期解.
关键词:
(3+1)维Nizhnik-Novikov-Veselov方程
非线性Klein-Gordon方程
孤子解
周期解 相似文献
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In this paper, we improve some key steps in the homogeneous balance method (HBM), and propose a modified homogeneous balance
method (MHBM) for constructing multiple soliton solutions of the nonlinear partial differential equation (PDE) in a unified
way. The method is very direct and primary; furthermore, many steps of this method can be performed by computer. Some illustrative
equations are investigated by this method and multiple soliton solutions are found. 相似文献
15.
We show how the Implicit Regularization Technique (IRT) can be used for the perturbative renormalization of a simple field theoretical model generally used as a test theory for new techniques. While IRT has been applied successfully in many problems involving symmetry-breaking anomalies and nonabelian gauge groups, all at one-loop level, this is the first attempt at a generalization of the technique for perturbative renormalization. We show that the overlapping divergent loops can be given a completely algebraic treatment. We display the connection between renormalization and counterterms in the Lagrangian. The algebraic advantages make IRT worth studying for perturbative renormalization of gauge theories. 相似文献
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Starting from local coupled Hirota equations,we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz–Kaup–Newell–Segur scattering problem.The Lax integrability of the nonlocal Hirota equation is also guaranteed by existence of the Lax pair.By Lax pair,an n-fold Darboux transformation is constructed for the nonlocal Hirota equation by which some types of exact solutions are found.The solutions with specific properties are distinct from those of the local Hirota equation.In order to further describe the properties and the dynamic features of the solutions explicitly,several kinds of graphs are depicted. 相似文献
18.
<正>In this paper,a variable-coefficient modified Korteweg-de Vries(vc-mKdV) equation is considered.Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function,then the one and two periodic wave solutions are presented,and it is also shown that the soliton solutions can be reduced from the periodic wave solutions. 相似文献
19.
Yoshimasa Matsuno 《Physics letters. A》2011,375(34):3090-3094
The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit. 相似文献
20.
We present a simple derivation of classes of early-time solutions of the Smoluchowski equation in the presence of boundaries, simplifying and generalizing an analysis by van Kampen. 相似文献