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 共查询到19条相似文献,搜索用时 93 毫秒
1.
沈守枫 《物理学报》2006,55(11):5606-5610
寻找高维可积模型是非线性科学中的重要课题.利用无穷维Virasoro对称子代数[σ(f1),σ(f2)]=σ(f1f2-f2f1)和向量场的延拓结构理论,能够得到各种高维模型.选取一些特殊的实现,可以给出具有无穷维Virasoro对称子代数意义下的高维微分可积模型.把该方法推广到微分-差分模型上,构造出具有弱多线性变量分离可解性的(3+1)维类Toda晶格.另外,该模型的一个约化方程为具有多线性变量分离可解性的(2+1)维特殊Toda晶格.连续运用对称约化方法可以得到此特殊Toda晶格的一个(1+1)维约化方程具有多线性变量分离可解性.因为得到的精确解里含有低维任意函数,从而可以构造出丰富地局域激发模式,如dromion解,lump解,环孤子解,呼吸子解,瞬子解,混沌斑图和分形斑图等等. 关键词: Virasoro代数 微分-差分模型 变量分离 局域激发模式  相似文献   

2.
用Riccati方程构造非线性差分微分方程新的精确解   总被引:3,自引:0,他引:3       下载免费PDF全文
把Riccati方程应用到非线性差分微分方程求解领域,并相结合与一种函数变换,借助符号计算系统Mathematica构造了修正的Volterra方程和一般格子方程新的精确孤立波解和三角函数解. 关键词: Riccati方程 函数变换 非线性差分微分方程 孤立波解  相似文献   

3.
一种修正Volterra链的精确解   总被引:1,自引:0,他引:1       下载免费PDF全文
张善卿 《物理学报》2007,56(4):1870-1874
给出一种构造非线性微分差分方程精确解的方法.利用该方法并借助计算机代数系统Maple,获得了一种修正的Volterra链的形式丰富的精确解.该方法也可应用于其他的微分差分方程(组). 关键词: 微分差分方程 精确解 符号计算  相似文献   

4.
两类非线性方程的精确解   总被引:7,自引:0,他引:7       下载免费PDF全文
利用行波约化方法,并借助于一维立方非线性Klein-Gordon方程的精确解,求出了(1+1)维Zakharov方程组、变系数Korteweg-de Vries方程的一些精确解- 关键词: 行波约化方法 一维立方非线性Klein-Gordon方程 (1+1)维Zakharov方程组 变系数Korteweg-de Vries方程  相似文献   

5.
杨征  马松华  方建平 《物理学报》2011,60(4):40508-040508
在符号计算软件Maple的帮助下,利用改进的Riccati方程映射法得到了(2+1)维Zakharov-Kuznetsov方程(ZK)的新显式精确解. 根据得到的解,研究了ZK方程的特殊孤子结构. 关键词: 改进的Riccati方程映射法 Zakharov-Kuznetsov方程 精确解 孤子结构  相似文献   

6.
(2+1)维非线性Burgers方程变量分离解和新型孤波结构   总被引:6,自引:0,他引:6       下载免费PDF全文
徐昌智  张解放 《物理学报》2004,53(8):2407-2412
利用变量分离方法,获得了(2+1)维非线性Burgers方程的变量分离解.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, 因而精确解中含有三个任意函数(其中一个为条件函数),适当地选择任意函数,可以获得多种形状的扭状孤波解、周期性孤子解和格子型孤波解. 关键词: 变量分离解 非线性波方程 (2+1)维  相似文献   

7.
用格子Boltzmann方法模拟MKDV方程   总被引:16,自引:0,他引:16       下载免费PDF全文
用精确到0(ε)的5速格子Boltzmann模型模拟MKDV方程:ut+6u2ux+uxxx=0,并与MKDV方程的孤子解比较,二者精确吻合. 关键词: 格子Boltzmann方法 MKDV方程 孤子解  相似文献   

8.
套格图桑  白玉梅 《物理学报》2012,61(13):130202-130202
辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bäcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解.  相似文献   

9.
变系数(2+1)维Broer-Kaup方程新的类孤子解   总被引:1,自引:0,他引:1  
基于齐次平衡原则和分离变量法的思想,通过两个推广的Riccati方程组和Mathematica软件,求出了变系数(2+1)维Broer-kaup方程的一些精确解,包括各种类孤立波解、类周期解,其中许多解是新的.  相似文献   

10.
非线性离散微分方程的双曲函数法求解   总被引:7,自引:0,他引:7       下载免费PDF全文
朱加民 《中国物理》2005,14(7):1290-1295
本文推广了双曲函数方法用于求解非线性离散系统。求解离散的(2+1)维Toda系统和离散的mKdV系统,成功地得到了离散钟型孤立子、离散冲击波型孤立子及一些新的精确行波解。  相似文献   

11.
In this paper, we generalize the extended tanh-function approach, which used to find new exact travelling wave solutions of nonlinear partial differential equations (NPDES) or coupled nonlinear partial differential equations, to nonlinear differential-difference equations (NDDES). As illustration, we discuss some Toda lattice equations, and solitary wave and periodic wave solutions of these Toda lattice equations are obtained by means of the extended tanh-function approach. PACS numbers: 05.45.Yv, 02.30.Jr, 02.30.Ik.  相似文献   

12.
求解非线性差分方程孤立波解的直接代数法   总被引:10,自引:0,他引:10       下载免费PDF全文
推广了求解非线性差分方程孤立波解的直接代数法.用此方法研究了Hybrid晶格方程,借助于符号计算Maple,得到它的新孤波解.这种方法也可用于求解其他的差分方程. 关键词: 微分-差分方程 Hybrid晶格方程 行波解 孤  相似文献   

13.
A new (2 1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1 1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2 1)-dimensional lattice equation are explicitly obtained by the Darboux transformation.  相似文献   

14.
In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established.  相似文献   

15.
In this article a brief review of the theory of one-dimensional nonlinear lattice is presented. Special attension is paid for the lattice of particles with exponential interaction between nearest neighbors (the Toda lattice). The historical exposition of findings of the model system, basic equations of motion, special solutions, and the general method of solutions are given as chronologically as possible. Some reference to the Korteweg-de Vries equation is also given. The article consists of three parts. Firstly, the idea of dual system is presented. It is shown that the roles of masses and springs of a harmonic linear chain can be exchanged under certain condition without changing the eigenfrequencies. Secondly, the idea is applied to the anharmonic lattice and an integrable lattice with exponential interaction force between adjacent particles is obtained. Special solutions to the equations of motion and general method of solution are shown. In the last part, some studies on the Yang-Yang’s thermodynamic formalism is given.  相似文献   

16.
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology.Such problems are presented as nonlinear differential–difference equations.The proposed method is based on the Laplace transform with the homotopy analysis method(HAM).This method is a powerful tool for solving a large amount of problems.This technique provides a series of functions which may converge to the exact solution of the problem.A good agreement between the obtained solution and some well-known results is obtained.  相似文献   

17.
Zene Horii   《Physica A》2005,350(2-4):349-378
To establish mass transport theory on nonlinear lattices, we formulate the Korteweg–deVries (KdV) equation and the Burgers equation using the flow variable representation so as to facilitate comparison with the Boltzmann equation and with the Cahn–Hilliard equation in classical statistical mechanics. We also study Toda lattice microdynamics using the Flaschka representation, and compare with the Liouville equation. Like the linear diffusion equation, the Boltzmann equation and the Liouville equation are to be solved for a distribution function, which is intrinsically probabilistic. Transport theory in linear systems is governed by the isotropic motions of the kinetic equations. In contrast, the KdV perturbation equation derived from the Toda lattice microdynamics expresses hydrodynamic mass transport. The KdV equation in hydrodynamics and the Burgers equation in thermodynamics do not involve a probability distribution function. The nonlinear lattices do not retain isotropy of the mass transport equations. In consequence, it is proposed that in the presence of hydrodynamic flows to the left, KdV wave propagation proceeds to the right. This basic property of the KdV system is extended to thermodynamics in the Burgers system. These features arise because linear systems are driven towards an equilibrium by molecular collisions, whereas the inhomogeneities of the nonlinear lattices are generated by the potential energy of interaction. Diffusion as expressed by the Burgers equation is governed not only by a chemical potential, but also by the Toda lattice potential energy.  相似文献   

18.
Combining Adomian decomposition method (ADM) with Pade approximants, we solve two differentiaidifference equations (DDEs): the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.  相似文献   

19.
In this paper, we apply the source generation procedure to the coupled 2D Toda lattice equation (also called Pfaffianized 2D Toda lattice), then we get a more generalized system which is the coupled 2D Toda lattice with self-consistent sources (p-2D TodaESCS), and a pfaffian type solution of the new system is given. Consequently, by using the reduction of the pfaffian solution to the determinant form, this new system can not only be reduced to the 2D TodaESCS, but be reduced to the coupled 2D Toda lattice equation. This result indicates that the p-2D TodaESCS is also a pfaffian version of the 2D TodaESCS, which implies the commutativity between the source generation procedure and Pfaffianization is valid to the semi-discrete soliton equation.  相似文献   

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