共查询到20条相似文献，搜索用时 78 毫秒
1.
给出了一类将微分多项式系统关于抽象对合延拓方向约化成对合特征集的算法. 该算法统一了已有的基于Riquier方法和Thomas方法及Pommaret方法延拓方程的算法. 采用我们及其他研究者最近发现的新延拓方向, 给出了计算对合特征集的新方法. 实践表明, 这些新方法可以用于简化Wu-Ritt特征集方法的计算程序. 相似文献
2.
从微分代数的角度出发,借助于吴微分特征集理论,对于线性偏微分方程组,给出了判定它的解的完备性的一个符号计算方法.这个算法是一个机械化的算法,借助于符号计算软件Maple,可以在计算机上实现. 相似文献
3.
本文讨论高阶ＭＤＷＷ方程的Ｌａｘ对，在位势与特征函数之间的约束条件下，Ｌａｘ系统被非线性化成为有限维Ｌｉｏｕｖｉｌｌｅ完全可积系统．并且获得了高阶ＭＤＷＷ方程解的对合表示． 相似文献
4.
本文在位势与特征函数之间的Neumann约束条件下,经典Boussinesq族的Lax对被非线性化成为自然相容的Lax系统;而且,其为Liouville完全可积的Hamiltonian系统,同时获得了Boussinesq方程解的对合表示。 相似文献
5.
本文参照代数Grobner基的思想,提出线性齐次偏微分方程组的既约化基的概念, 并给出了线性齐次偏微分方程组的既约化基的唯一性定理. 相似文献
6.
本作研究了一类拟线性偏微分方程组在不同的外边界条件(无穷大外边界，封闭外边界，定值外边界)和随机时间变化的内边界条件下的初值问题在Laplace空间的解的形式相似性，它能很好地帮助我们认识模型遵从的内在规律及设计相应的应用软件． 相似文献
7.
本文是在[1]-[10]工作的基础上,在复域中讨论P阶线性偏微分方程组柯西问题(A)(∂ pu)/∂t p-B 1(z)(∂ p-1u)/∂t p-1-B 2（z）（∂ p-2u）/∂t p-2-…-B p-1（z）（∂u）/∂t=Du+∑ j=1ma j（z）t p（∂ tu）/∂t it=0=φ i(z)(i=0,1,…p-1)(方程中m=∞时,级数在原点附近一致收敛)解析解的结构,获得了方程组的系数矩阵B i(z)(i=1,2,…,p-1)及微分算子D之间的相互可易,部分可易和互不可易的诸情况下的一般解析解的级数形式显式表达式。 相似文献
8.
本文给出了三阶交系数线性微分方程具有特解 的充要条件,并由此得到了一类三阶交系数线性微分方程的可积条件。 相似文献
10.
线性微分方程在物理学,力学及控制论中有着广泛应用,近年来在国内外一些重要刊物上发表多篇有关求微分方程精确解的论文。本文在这些论文的基础上,借助于Lcibniz求导公式及变换组法,进而提出了高阶非线性常微分方程组的求解法,于是论证了它的可积性,所得结果是相应文献结果的推广。 相似文献
11.
This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations. 相似文献
12.
Using the Spencer-Goldschmidt version of the Cartan-Kähler theorem, we give conditions for (local) existence of conservation laws for analytical quasi-linear systems of two independent variables. This result is applied to characterize the recursion operator (in the sense of Magri) of completely integrable systems. 相似文献
13.
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
14.
In an American Mathematical Society Memoir, published in 2003, the authors Everitt and Markus apply their prior theory of symplectic algebra to the study of symmetric linear partial differential expressions, and the generation of self-adjoint differential operators in Sobolev Hilbert spaces. In the case when the differential expression has smooth coefficients on the closure of a bounded open region, in Euclidean space, and when the region has a smooth boundary, this theory leads to the construction of certain self-adjoint partial differential operators which cannot be defined by applying classical or generalized conditions on the boundary of the open region. This present paper concerns the spectral properties of one of these unusual self-adjoint operators, sometimes called the ``Harmonic' operator. The boundary value problems considered in the Memoir (see above) and in this paper are called regular in that the cofficients of the differential expression do not have singularities within or on the boundary of the region; also the region is bounded and has a smooth boundary. Under these and some additional technical conditions it is shown in the Memoir, and emphasized in this present paper, that all the self-adjoint operators considered are explicitly determined on their domains by the partial differential expression; this property makes a remarkable comparison with the case of symmetric ordinary differential expressions. In the regular ordinary case the spectrum of all the self-adjoint operators is discrete in that it consists of a countable number of eigenvalues with no finite point of accumulation, and each eigenvalue is of finite multiplicity. Thus the essential spectrum of all these operators is empty. This spectral property extends to the present partial differential case for the classical Dirichlet and Neumann operators but not to the Harmonic operator. It is shown in this paper that the Harmonic operator has an eigenvalue of infinite multiplicity at the origin of the complex spectral plane; thus the essential spectrum of this operator is not empty. Both the weak and strong formulations of the Harmonic boundary value problem are considered; these two formulations are shown to be equivalent. In the final section of the paper examples are considered which show that the Harmonic operator, defined by the methods of symplectic algebra, has a domain that cannot be determined by applying either classical or generalized local conditions on the boundary of the region. 相似文献
15.
本文简单介绍了吴微分特征列和Janet基,利用线性齐次微分方程组既约化基的概念,证明了线性齐次偏微分方程组的正规化的吴微分特征列和正规化的、自约化的Janet基均是既约化基,从而由既约化基的唯一性,得到了它们的等价性定理。 相似文献
16.
In this paper we investigate the solvability of linear systems of partial differential equations with constant coefficients in a field of positive characteristic. In particular, we prove that consistence and compatibility are equivalent, which answers a question of Ehrenpreis and extends a result of Jia. The problem of uniqueness is also considered. 相似文献
17.
Under the Bargmann constrained condition, the spatial part of a new Lax pairof the higher order MkdV equation is nonlinearized to be a completely integrable system(R^2N,dp∧dq, H0=1/2F0)(F0=〈Aq,p〉 〈Ap, p〉 〈p,q〉^2). While the nonlinearization of the time part leads to its N-involutive system (Fm). 相似文献
18.
We compare three different ways of checking the Jacobi identity for weakly nonlocal Poisson brackets using the theory of distributions, pseudo-differential operators, and Poisson vertex algebras, respectively. We show that the three approaches lead to similar computations and same results. 相似文献
19.
本文直接递归地生成了一列Liouville可积的有限维Hamilton系统族,给出了其一串对合的公共运动积分和一组对合的生成元． 相似文献
20.
本文通过一个特征值问题的非线性化,得到了一个Bargmann系统并证明了它是Liouville意义下的完全可积系统,并给出了与这个特征值问题相联系的演化方程解的对合表示。 相似文献
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