共查询到20条相似文献,搜索用时 62 毫秒
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应用经典无穷小Lie群方法和CK直接方法得到了非线性弦振动方程的新的相似约化和新的精确解。应用经典Lie群方法将非线性弦振动方程约化成了第三类和第四类椭圆方程,同时得到了非线性弦振动方程的显式类孤立波解。进而,应用不涉及群论的CK直接方法得到了非线性弦振动方程的更为一般的相似约化。 相似文献
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本文研究双组分Degasperis-Procesi方程的有界行波解。利用平面动力系统的分岔理论,分析了双组分Degasperis-Procesi方程对应行波系统在参数平面不同区域的分岔相图。进而,依据动力系统相轨中的同宿轨、周期轨与非线性波动方程的孤立波解、周期波解之间的关系,在一定的参数条件下,获得了双组份Degasperis-Procesi方程的孤立波解和周期波解,并借助数值模拟给出了部分解的图像。 相似文献
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WBK浅水波方程是数学物理中的重要方程之一,对其研究有重要意义。经典方法都是在确定状态下研究波方程的性质和精确求解。随机分析和白噪声理论的建立和发展为波方程的研究提供了新的内容、方法和工具,因此,研究随机状态下波方程就成为可能。本文就是研究随机状态下WBK浅水波方程的精确求解问题:在Kondratiev分布空间(S)-1中,利用Hermite变换和齐次平衡法研究Wick-型随机WBK浅水波方程的精确求解,给出其白噪声泛函解,并给出了该方程在系数F(t)取不同白噪声泛函时的几个例子。 相似文献
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组合KdV-Burgers方程的精确解 总被引:7,自引:1,他引:6
用直接方法和假设方法的一种结合得到了组合KdV-Burgers方程的一些显式精确解。包括孤波解、奇异行波解和三角函数状周期波解。这个方程的一些特别重要的情形如组合KdV方程,mKdV-Burgers方程及mKdV方程等也可用此方法精确求解。 相似文献
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通过行波约化一类(3+1)维非线性波动方程和建立与立方非线性Klejn-Gordon方程间变换的联系,由此得到其孤立波解和周期解。 相似文献
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Davey-Stewartson方程描述了有限深度的水中水波的运动,它的第一种类型称为(Davey-Stewartson I)是椭圆一双曲型方程。在物理学中,微分方程的精确解对考察非线性现象起着非常重要的作用,为了揭示Davey-Stewartson I方程的运动性质,本文研究它的精确周期解。应用F-代数方法并通过一个高阶辅助微分方程,获得了Davey-Stewartson I方程的一系列新的精确周期解,包括三角函数周期解,Jacobi椭圆函数周期解。 相似文献
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Anne Duval Michèle Loday-Richaud 《Applicable Algebra in Engineering, Communication and Computing》1992,3(3):211-246
We apply the Kovacic algorithm to some families of special functions, mainly the hypergeometric one and that of Heun, in order to discuss the existence of closed-form solutions. We begin by giving a slightly modified version of the Kovacic algorithm and a sketch proof. 相似文献
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从三维非线性理论导出,任意曲线坐标系中任意壳体的几何非线性微分方程,并修正K.Washizu的公式,以期得到更加准确的稳定方程。 相似文献
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随机系统能稳性的一个注记 总被引:2,自引:0,他引:2
研究随机系统dx=(Ax-Bu)dt-(Cx+Du)dW的能稳性,首先组出了系统能稳性的一个充分必要条件,并通过构造一个反例指出了以往文献中的一个错误。 相似文献
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从三维非线性理论导出,任意曲线坐标系中任意壳体的几何非线性微分方程,并修正K.Washizu的公式,以期得到更加准确的稳定方程。 相似文献
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Yih-Hsing Pao Li-Sheng Wang Kuo-Ching Chen 《International Journal of Engineering Science》2011,49(12):1502-1516
A fundamental variational principle, called the Principle of Virtual Power, is proposed in this paper to govern the irreversible thermomechanical processes for a material body. The principle and the corresponding variational equation of virtual velocity are formulated by integrating the classical field theories of continuum mechanics and thermodynamics. From the variational equation, we establish simultaneously the balance equations of linear momentum, of angular momentum, and of virtual internal power by applying the procedure of relaxation in Lagrangian mechanics. By assuming different types of system functions for internal power consisting of internal energy and newly introduced working dissipation, we are able to derive the constitutive equations for gas, liquid, or solid and the Fourier equation of heat conduction from the balance of virtual internal power. The combination of the law of conservation of mass, the first law of thermodynamics, and the proposed principle forms a complete set of fundamental principles for the thermomechanics of deformable bodies. 相似文献
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本文以 Poisson 方程为例,在不对节点进行重新排列的前提下,通过求解较低维数的矩阵方程,对交替方向隐式迭代格式进行了改进,降低了程序实现难度.以 Gauss 消去法为例,对改进的交替方向隐式迭代格式的计算量进行估计,发现改进的交替方向隐式迭代格式大大减少了计算量,并进一步证明了改进的交替方向隐式迭代格式与经典的交替方向隐式迭代格式的等价性.数值算例验证了改进的交替方向隐式迭代格式与经典的交替方向隐式迭代格式的等价性和改进的交替方向隐式迭代格式在计算量等方面的优越性. 相似文献
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Reza Haj Mohammad Jafar 《International Journal of Engineering Science》2011,49(5):378-385
The electric current flowing across two parallel plates that touch each other over a circular contact is calculated. The change in the physical properties due to temperature rise caused by Joule heating is taken into account so that the current is not linearly proportional to the voltage difference. The resistance is calculated and an accurate approximation for the resistance, based on minimizing the power, is presented. 相似文献
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N. E. DOWLING C. A. CALHOUN A. ARCARI 《Fatigue & Fracture of Engineering Materials & Structures》2009,32(3):163-179
Mean stress effects in finite-life fatigue are studied for a number of sets of experimental data for steels, aluminium alloys and one titanium alloy. Specifically, the agreement with these data is examined for the Goodman, Morrow, Smith–Watson–Topper and Walker equations. The Goodman relationship is found to be highly inaccurate. Reasonable accuracy is provided by the Morrow and by the Smith–Watson–Topper equations. But the Morrow method should not be used for aluminium alloys unless the true fracture strength is employed, instead of the more usual use of the stress-life intercept constant. The Walker equation with its adjustable fitting parameter γ gives superior results. For steels, γ is found to correlate with the ultimate tensile strength, and a linear relationship permits γ to be estimated for cases where non-zero mean stress data are not available. Relatively high-strength aluminium alloys have γ≈ 0.5, which corresponds with the SWT method, but higher values of γ apply for relatively low-strength aluminium alloys. For both steels and aluminium alloys, there is a trend of decreasing γ with increasing strength, indicating an increasing sensitivity to mean stress. 相似文献
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本文首先讨论了差映射的一个映射性质:某元有无映射原象等价于映射象集是否包含此元,等价于以此元为象的映射方程的解是否存在.若有两个映射,其中一个映射的象集较大,另一个映射的象集较小,则在一定条件下,可以确定此二映射的差映射象集包含一集合,此集合的差映射原象非空,以此集合中的元为映射象的差映射方程的解存在.其次,我们运用此结论讨论了几个微分方程、差分方程多解的存在性. 相似文献