共查询到20条相似文献,搜索用时 171 毫秒
1.
给出了一个确定含参数偏微分方程(组)的完全对称分类微分特征列集算法,该算法能够直接、系统地确定偏微分方程(组)的完全对称分类.用给出的算法获得了含任意函数类参数的线性和非线性波动方程完全势对称分类.这也是微分形式特征列集算法(微分形式吴方法)在微分方程领域中的新应用. 相似文献
2.
一类非线性波动方程的势对称分类 总被引:1,自引:0,他引:1
先给出了含有一个任意函数的线性波动方程的古典和势对称的完全分类.然后,在此基础上给出了含有两个任意函数的一类非线性波动方程的两种情形势对称分类,得到了该方程的新势对称.在处理对称群分类问题的难点-求解确定方程组时我们提出了微分形式吴方法算法,克服了以往难于处理的困难.在整个计算过程中反复使用了吴方法,吴方法起到了关键的作用. 相似文献
3.
4.
5.
首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性. 相似文献
6.
7.
微分方程(组)对称向量的吴-微分特征列算法及其应用 总被引:9,自引:0,他引:9
朝鲁 《数学物理学报(A辑)》1999,19(3):326-332
给出(偏)微分方程(组)(PDEs)对称向量的吴-微分特征列集(消元)算法理论.把古典和非古典PDEs对称问量的计算问题统-在吴-微分特征列理论框架之下处理.给出了产生PDEs对称向量的无穷小方程和验证已知向量为PDES对称向量的机械化原理,理论上彻底克服了传统算法中的缺陷并为计算PDEs对称向量提供了一种新算法.用计算机代数系统mathematica编制了相应的软件包,具体实现了该算法.作为应用给出了Burgers方程的非古典对称向量的完整解答. 相似文献
8.
基于微分特征集理论和算法,提出在一定条件下判定偏微分方程(组)非古典对称存在性的机械化方法.该方法对Clarkson P A提出的关于偏微分方程(组)的非古典对称的公开问题给出了部分回答,为完全解决该问题提供了一个思路.通过若干个发展方程的非古典对称的确定说明了该方法的有效性. 相似文献
9.
研究一类微分-差分方程组的对称和等价群变换.采取内禀的无穷小算子方法,给出了方程组的内禀对称和等价群变换.为结合抽象Lie代数结构,给方程完全分类提供了理论基础. 相似文献
10.
微分多项式系统的约化算法理论 总被引:8,自引:0,他引:8
本文中,作者推广了纯代数形式的特征列集理论(吴方法)为微分形式的相应理论,即建立了在机器证明了诸多微分问题中非常重要的微分多项式组的约化算法理论。引入了一些新的概念和观点使函数微分(导数)具有直观的代数几何表示。给出了Coherent条件下的特征列集的算法。给出的算法易于在计算机上实现并适合应用于广泛的微分问题,如微分方程对称计算,各种微分关系的自动推理等问题。 相似文献
11.
In this paper, based on differential characteristic set theory and the associated algorithm (also called Wu?s method), an algorithmic method is presented to decide on the existence of a nontrivial non-classical symmetry of a given partial differential equation without solving the corresponding nonlinear determining system. The theory and algorithm give a partial answer for the open problem posed by P.A. Clarkson and E.L. Mansfield in [21] on non-classical symmetries of partial differential equations. As applications of our algorithm, non-classical symmetries and corresponding invariant solutions are found for several evolution equations. 相似文献
12.
Scott W. McCue I. Kenneth Johnpillai James M. Hill 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,38(5):1061-1083
A variety of modelling approaches currently exist to describe and predict the diverse behaviours of granular materials. One
of the more sophisticated theories is hypoplasticity, which is a stress-rate theory of rational continuum mechanics with a
constitutive law expressed in a single tensorial equation. In this paper, a particular version of hypoplasticity, due to Wu
[2], is employed to describe a class of one-dimensional granular deformations. By combining the constitutive law with the
conservation laws of continuum mechanics, a system of four nonlinear partial differential equations is derived for the axial
and lateral stress, the velocity and the void ratio. Under certain restrictions, three of the governing equations may be combined
to yield ordinary differential equations, whose solutions can be calculated exactly. Several new analytical results are obtained
which are applicable to oedometer testing. In general this approach is not possible, and analytic progress is sought via Lie
symmetry analysis. A complete set or “optimal system” of group-invariant solutions is identified using the Olver method, which
involves the adjoint representation of the symmetry group on its Lie algebra. Each element in the optimal system is governed
by a system of nonlinear ordinary differential equations which in general must be solved numerically. Solutions previously
considered in the literature are noted, and their relation to our optimal system identified. Two illustrative examples are
examined and the variation of various functions occuring in the physical variables is shown graphically. 相似文献
13.
14.
Scott W. McCue I. Kenneth Johnpillai James M. Hill 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(6):1061-1083
A variety of modelling approaches currently exist to describe and predict the diverse behaviours of granular materials. One
of the more sophisticated theories is hypoplasticity, which is a stress-rate theory of rational continuum mechanics with a
constitutive law expressed in a single tensorial equation. In this paper, a particular version of hypoplasticity, due to Wu
[2], is employed to describe a class of one-dimensional granular deformations. By combining the constitutive law with the
conservation laws of continuum mechanics, a system of four nonlinear partial differential equations is derived for the axial
and lateral stress, the velocity and the void ratio. Under certain restrictions, three of the governing equations may be combined
to yield ordinary differential equations, whose solutions can be calculated exactly. Several new analytical results are obtained
which are applicable to oedometer testing. In general this approach is not possible, and analytic progress is sought via Lie
symmetry analysis. A complete set or “optimal system” of group-invariant solutions is identified using the Olver method, which
involves the adjoint representation of the symmetry group on its Lie algebra. Each element in the optimal system is governed
by a system of nonlinear ordinary differential equations which in general must be solved numerically. Solutions previously
considered in the literature are noted, and their relation to our optimal system identified. Two illustrative examples are
examined and the variation of various functions occuring in the physical variables is shown graphically.
Received: February 3, 2004; revised: June 2, 2004 相似文献
15.
Four symbolic programs, in Macsyma or Mathematica language, are presented. The first program tests forthe existence of solitons for nonlinear PDEs. It explicitly constructs solitons using Hirota's bilinear method. In the second program, the Painlevé integrability test for ODEs and PDEs is implemented. The third program provides an algorithm to compute conserved densities for nonlinear evolution equations. The fourth software package aids in the computation of Lie symmetries of systems of differential and difference-differential equations. Several examples illustrate the capabilities of the software.Research supported in part by NSF under Grant CCR-9300978. 相似文献
16.
非线性波方程准确孤立波解的符号计算 总被引:75,自引:0,他引:75
该文将机械化数学方法应用于偏微分方程领域,建立了构造一类非线性发展方程孤立波解的一种统一算法,并在计算机数学系统上加以实现,推导出了一批非线性发展方程的精确孤立波解.算法的基本原理是利用非线性发展方程孤立波解的局部性特点,将孤立波表示为双曲正切函数的多项式.从而将非线性发展方程(组)的求解问题转化为非线性代数方程组的求解问题.利用吴文俊消元法在计算机代数系统上求解非线性代数方程组,最终获得非线性发展方程(组)的准确孤立波解. 相似文献
17.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2212-2219
In this paper, we study conservation laws for some partial differential equations. It is shown that interesting conserved quantities arise from multipliers by using homotopy operator that is a powerful algorithmic tool. Furthermore, the invariance properties of the conserved flows with respect to the Lie point symmetry generators are investigated via the symmetry action on the multipliers. Furthermore, the similarity reductions and some exact solutions are provided. 相似文献
18.
A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method 下载免费PDF全文
M. F. El‐Sayed G. M. Moatimid M. H. M. Moussa R. M. El‐Shiekh F. A. H. El‐Shiekh A. A. El‐Satar 《Mathematical Methods in the Applied Sciences》2015,38(17):3670-3677
In this paper,we applied the Painlevé property test on Krook‐Wu model of the nonlinear Boltzmann equation (p = 1). As a result, by using Bäcklund transformation, we obtained three solutions two of them were known earlier, while the third one is new and more general, we have also two reductions one of them is Abel's equation. Also, Lie‐group method is applied to the (p + 1)th Boltzmann equation. The complete Lie algebra of infinitesimal symmetries is established. Three nonequivalent sub‐algebraic of the complete Lie algebra are used to investigate similarity solutions and similarity reductions in the form of nonlinear ordinary equations for (p + 1)th Boltzmann equation; we obtained two general solutions for (p + 1)th Boltzmann equation and new solutions for Krook‐Wu model of Boltzmann equation (p = 1). Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
M. C. Nucci 《Theoretical and Mathematical Physics》2007,151(3):851-862
In addition to the reduction method, we present a novel application of Jacobi’s last multiplier for finding Lie symmetries
of ordinary differential equations algorithmically. These methods and Lie symmetries allow unveiling the hidden linearity
of certain nonlinear equations that are relevant in physics. We consider the Einstein-Yang-Mills equations and Calogero’s
many-body problem in the plane as examples.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 495–509, June, 2007. 相似文献
20.
This is the first in a series of papers devoted to the development and applications of a new general theory of moving frames. In this paper, we formulate a practical and easy to implement explicit method to compute moving frames, invariant differential forms, differential invariants and invariant differential operators, and solve general equivalence problems for both finite-dimensional Lie group actions and infinite Lie pseudo-groups. A wide variety of applications, ranging from differential equations to differential geometry to computer vision are presented. The theoretical justifications for the moving coframe algorithm will appear in the next paper in this series. 相似文献