共查询到19条相似文献,搜索用时 140 毫秒
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Finite symmetry transformation group of the Konopelchenko-Dubrovsky equation from its Lax pair 下载免费PDF全文
Starting from a weak Lax pair,the general Lie point symmetry group of the Konopelchenko-Dubrovsky equation is obtained by using the general direct method.And the corresponding Lie algebra structure is proved to be a Kac-Moody-Virasoro type.Furthermore,a new multi-soliton solution for the Konopelchenko-Dubrovsky equation is also given from this symmetry group and a known solution. 相似文献
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从质点系的牛顿动力学方程出发,引入系统的高阶速度能量,导出完整力学系统的高阶Lagrange方程、高阶Nielsen方程以及高阶Appell方程,并证明了完整系统三种形式的高阶运动微分方程是等价的.结果表明,完整系统高阶运动微分方程揭示了系统运动状态的改变与力的各阶变化率之间的联系,这是牛顿动力学方程以及传统分析力学方程不能直接反映的.因此,完整系统高阶运动微分方程是对牛顿动力学方程及传统Lagrange方程、Nielsen方程、Appell方程等二阶运动微分方程的进一步补充.
关键词:
高阶速度能量
高阶Lagrange方程
高阶 Nielsen方程
高阶Appell方程 相似文献
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非均匀反射全息图的理论分析 总被引:3,自引:2,他引:1
本文对非均匀反射全息图进行了理论分析.在考虑记录介质吸收的情况下,通过适当的变换,将耦合波理论中由两个线性微分方程构成的微分方程组——耦合波方程,化为一个变系数非线性微分方程——黎卡提方程.并对方程的性质进行了分析.通过数值解,发现了一些新的很有意义的现象. 相似文献
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为了构造高维非线性发展方程的无穷序列类孤子新解, 研究了二阶常系数齐次线性常微分方程, 获得了新结论. 步骤一, 给出一种函数变换把二阶常系数齐次线性常微分方程的求解问题转化为一元二次方 程和Riccati方程的求解问题. 在此基础上, 利用Riccati方程解的非线性叠加公式, 获得了二阶常系数齐次线性常微分方程的无穷序列新解. 步骤二, 利用以上得到的结论与符号计算系统Mathematica, 构造了(2+1)维广义Calogero-Bogoyavlenskii-Schiff (GCBS)方程的无穷序列类孤子新解.
关键词:
常微分方程
非线性叠加公式
高维非线性发展方程
无穷序列类孤子新解 相似文献
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Recently, fractional calculus has attracted much attention since it plays an important role in many fields of science and
engineering. Especially, the study on stability of fractional differential equations appears to be very important. In this
paper, a brief overview on the recent stability results of fractional differential equations and the analytical methods used
are provided. These equations include linear fractional differential equations, nonlinear fractional differential equations,
fractional differential equations with time-delay. Some conclusions for stability are similar to that of classical integer-order
differential equations. However, not all of the stability conditions are parallel to the corresponding classical integer-order
differential equations because of non-locality and weak singularities of fractional calculus. Some results and remarks are
also included. 相似文献
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A. I. Fomin 《Russian Journal of Mathematical Physics》2012,19(2):159-181
Linear differential operators with complex-valued infinitely differentiable coefficients, linear homogeneous systems of differential equations, and modules over algebras of scalar linear differential operators are considered. Linear differential changes of variables and homomorphisms of special quotient modules (differential homomorphisms) generated by these changes are studied. In terms of differential homomorphisms, relationships between Maxwell equations and equations of electromagnetic potential and between Dirac equations and the Klein-Gordon system of independent equations are described. It is proved that all ordinary nondegenerate linear homogeneous differential equations of some common order and the homogeneous normal systems of the same common order are differentially isomorphic. 相似文献
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Frobenius integrable decompositions are introduced for partial differential equations. A procedure is provided for determining a class of partial differential equations of polynomial type, which possess specified Frobenius integrable decompositions. Two concrete examples with logarithmic derivative Bäcklund transformations are given, and the presented partial differential equations are transformed into Frobenius integrable ordinary differential equations with cubic nonlinearity. The resulting solutions are illustrated to describe the solution phenomena shared with the KdV and potential KdV equations. 相似文献
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One-dimensional Jacobian elliptic quasi-exactly solvable second-order differential equations are obtained by introducing the
generalized third master functions. It is shown that the solutions of these differential equations are generating functions
for a new set of polynomials in terms of energy with factorization property. The roots of these polynomials are the same as
the eigenvalues of the differential equations. Some one-dimensional elliptic quasi-exactly quantum solvable models are obtained
from these differential equations.
相似文献
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This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewritten as 2n first-order differential equations. Secondly, the corresponding partial differential equations are obtained by potential integration method and the solution is expressed as a complete integral. Finally, the integral of the system is obtained. 相似文献
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Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split
system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex
heat equation, wave equation with dissipation, the nonlinear Burgers equation and nonlinear KdV equations. We split the Lie
symmetries of a complex partial differential equation in the real domain and obtain real Lie-like operators. Further, the
complex partial differential equation is split into two coupled or uncoupled real partial differential equations which constitute
a system of two equations for two real functions of two real variables. The Lie symmetries of this system are constructed
by the classical Lie approach. We compare these Lie symmetries with the split Lie-like operators of the given complex partial
differential equation for the examples considered. We conclude that the split Lie-like operators of complex partial differential
equations are not in general symmetries of the split system of real partial differential equations. We prove a proposition
that gives the criteria when the Lie-like operators are symmetries of the split system. 相似文献
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In this paper, a Birkhoff--Noether method of solving ordinary
differential equations is presented. The differential equations can
be expressed in terms of Birkhoff's equations. The first integrals
for differential equations can be found by using the Noether theory
for Birkhoffian systems. Two examples are given to illustrate the
application of the method. 相似文献
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The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions. 相似文献