共查询到19条相似文献,搜索用时 140 毫秒
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建立圆柱体任意两个截面间的一般黏弹性转动力学方程,讨论了相对转角的稳定性,由于此方程为变系数的二阶线性的非齐次常微分方程组,没有统一的求解方法.因此,针对其中的一类黏弹性系数求得其解.
关键词:
变系数方程的解
相对转角
稳定性 相似文献
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一类二阶线性变系数常微分方程的常系数化解法 总被引:1,自引:1,他引:0
利用线性方程对自变量的变换以及对未知函数的线性变换的不变性,导出一类二阶线性变系数常微分方程系数化的充要条件及所需的变换,给出求这类方程的显示解的简便方法。 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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为了构造非线性发展方程的无穷序列复合型类孤子新解, 进一步研究了G'(ξ)/G(ξ) 展开法. 首先, 给出一种函数变换, 把常系数二阶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. 然后, 利用Riccati方程解的非线性叠加公式, 获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解. 在此基础上, 借助符号计算系统Mathematica, 构造了改进的(2+1)维色散水波系统和(2+1)维色散长波方程的无穷序列复合型类孤子新精确解.
关键词:
G'(ξ)/G(ξ)展开法')" href="#">G'(ξ)/G(ξ)展开法
非线性叠加公式
非线性发展方程
复合型类孤子新解 相似文献
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脉冲半导体激光器电源电路分析 总被引:3,自引:1,他引:3
直接调制的大电流窄脉宽驱动电源是脉冲半导体激光器获得高峰值功率输出的重要保证。建立了脉冲半导体激光器驱动电源的等效电路及其LRC回路模型,对线性常系数二阶齐次微分方程的分析解进行了分析,并与实验结果做了比较。结果显示,当电源主要参数满足R≥2√L/C关系时,可获得较为理想的非振荡放电过程,实测脉冲波形及其特性与计算结果相符合。 相似文献
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矩阵及其特征值的应用十分广泛。本文讨论它们在求解线性微分方程组中的应用,给出了常系数线性微分方程组的解的指数矩阵表示方法。 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(3):283-298
Invariant linearization criteria for square systems of second-order quadratically nonlinear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in the first derivatives. It is shown that there are two branches for the linearization problem via point transformations for an arbitrary system of second-order ODEs and its reduction to the simplest system. One is when the system is at most cubic in the first derivatives. One obtains the equivalent of the Lie conditions for such systems. We explicitly solve this branch of the linearization problem by point transformations in the case of a square system of two second-order ODEs. Necessary and sufficient conditions for linearization to the simplest system by means of point transformations are given in terms of coefficient functions of the system of two second-order ODEs cubically nonlinear in the first derivatives. A consequence of our geometric approach of projection is a rederivation of Lie's linearization conditions for a single second-order ODE and sheds light on more recent results for them. In particular we show here how one can construct point transformations for reduction to the simplest linear equation by going to the higher space and just utilizing the coefficients of the original ODE. We also obtain invariant criteria for the reduction of a linear square system to the simplest system. Moreover these results contain the quadratic case as a special case. Examples are given to illustrate our results. 相似文献
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用函数和方程变换将二阶耦合线性微分方程组转化为一阶非线性类椭圆方程,并给出了一次和二次限定变换下方程组的Jacobi椭圆函数解析解,所得结果修正了文献中超导特例的近似解,进一步肯定了超导边界层电场的存在性.
关键词:
微分方程
Jacobi椭圆函数
解析解
超导 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(3):399-421
Abstract We investigate the Sundman symmetries of second-order and third-order nonlinear ordinary differential equations. These symmetries, which are in general nonlocal transformations, arise from generalised Sundman transformations of autonomous equations. We show that these transformations and symmetries can be calculated systematically and can be used to find first integrals of the equations. 相似文献
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G. Costanza 《Physica A》2012,391(6):2167-2181
The proof of a theorem that allows one to construct deterministic evolution equations from a set, with two subsets, containing two types of discrete stochastic evolution equation is developed. One subset evolves Markovianly and the other non-Markovianly. As an illustrative example, the deterministic evolution equations of quantum electrodynamics are derived from two sets of Markovian and non-Markovian stochastic evolution equations, of different type, after an average over realization, using the theorem. This example shows that deterministic differential equations that contain both first-order and second-order time derivatives can be derived after a Taylor series expansion of the dynamical variables. It is shown that the derivation of such deterministic differential equations can be done by solving a set of linear equations. Two explicit examples, the first containing updating rules that depend on one previous time step and the second containing updating rules that depend on two previous time steps, are given in detail in order to show step by step the linear transformations that allow one to obtain the deterministic differential equations. 相似文献
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Solitary Wave in Linear ODE with Variable Coefficients 总被引:1,自引:0,他引:1
In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained. 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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The symmetry reduction method based on the Fr′echet 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
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S. Esposito 《International Journal of Theoretical Physics》2002,41(12):2417-2426
We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed to reduce the degree of nonlinearity of the lower order equation. Some applications of these methods are carried out and, in particular, we show that second-order Emden–Fowler equations can be transformed into first-order Abel equations. The work presented here is a generalization of a method used by Majorana in order to solve the Thomas–Fermi equation. 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