共查询到20条相似文献,搜索用时 109 毫秒
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利用广义变分迭代方法研究了一类非线性发展扰动方程.首先引入一个泛函.然后求其变分,最后构造方程解的迭代关系式.得到了问题的近似解和精确解析解.
关键词:
发展方程
扰动
变分迭代 相似文献
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研究了一类非线性扰动Burgers方程的求解问题. 利用变分迭代方法, 首先引入一个泛函, 然后计算它的变分, 最后构造方程的迭代关系式, 得到了相应方程的孤子解的近似展开式. 相似文献
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研究了一类非线性尘埃等离子体孤波解. 首先构造一个变分迭代, 其次决定系统的初始近似, 最后通过变分迭代方法得到了对应模型的各次近似解.
关键词:
等离子体
变分迭代
近似解 相似文献
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The generalized variational principle of Herglotz type provides a variational method for describing nonconservative or dissipative processes. The purpose of this letter is to extend this variational principle to a first order linear nonholonomic system and study the conservation laws of the nonconservative nonholonomic system based on Herglotz variational problem. A new differential variational principle of the nonconservative nonholonomic system is proposed, which is based on Herglotz variational problem. And the differential equations of motion of the system are also obtained. Then, according to the condition for the invariance of the differential variational principle, the conservation theorem based on Herglotz variational problem for the nonconservative nonholonomic system are obtained. The theorem contains the conservation theorem of the nonconservative holonomic system as its special case, which can be reduced to the first Noether's theorem based on Herglotz variational problem under proper conditions. The inverse theorem of the conservation theorem is also provided and proved. An example is given to illustrate the application at the end of this letter. 相似文献
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The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out. 相似文献
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ZhenBang Kuang 《中国科学G辑(英文版)》2008,51(9):1390-1402
It is proposed that the universal thermodynamic energy variational principle is included in the first law of thermodynamics.
Some variational principles in the electroelastic media under finite deformation are derived from this universal thermodynamic
variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together
with the discussed electroelastic medium. For the variational principle of nonlinear electroelastic media the variation of
the electric potential is coupled with the virtual displacement, and the variation of the initial volume should be considered.
The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the
second order precision.
Supported by the National Natural Science Foundation of China (Grant No. 10472069) 相似文献
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The heat equation is re-studied in this Letter in view of variational theory. By the semi-inverse method, a variational principle for the heat conduction is obtained, which is first appeared in the literature. The physical understanding of the obtained variational principle still needs further explanation. 相似文献
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CHEN De-Fang SONG Yong-Shen CHEN Tian-Lun ZHENG Xi-Te HE Xiang-Hao XIAN Ding-Chang 《中国物理C(英文版)》1986,10(1):32-39
The relation between the saddle point approximation and the action variational method in the lattice gauge field theory is discussed. It is expounded that in the thermodynamical limit by using a trial action composed of mean fields, the variational approach leads to the results as well as the higher order corrections obtained in the saddle point approximation. It is also pointed out that order by order corrections to the variational approach can be worked out systematically in an improved variational approach. 相似文献
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It is widely accepted that a variational principle cannot be constructed for an arbitrary differential equation; a rigorous mathematical condition shows which equations can have a variational formulation. On the other hand, the importance for variational principles in various fields of physics resulted in several methods to circumvent this condition and to construct another type of variational principles for any differential equation. In this paper the common origin of the considered methods is investigated, and a generalized Hamiltonian formalism is formulated. Additionally, constructive algorithms are given by different methods to construct variational principles. Simple examples are presented to make construction methods more transparent: several Lagrangians are constructed for the different forms of the Maxwell equations and for the extended heat conduction equation. 相似文献
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Ji-Huan He 《Physics letters. A》2011,375(38):3362-3364
This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed. 相似文献