Boussinesq方程组的广义变分原理

半反推法是何吉欢为了寻求物理问题的变分原理而提出的,可避免由拉氏乘子法引起的临界变分现象. 应用半反推法分别获得了描述水波运动的两类Boussinesq方程组的一族广义变分原理,并验证了它们的正确性. 关键词： 半反推法 广义变分原理 Boussinesq方程组     

A short remark on fractional variational iteration method

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.     

Variational iteration method for solving biharmonic equations

By means of the variational iteration method the numerical solution of biharmonic equations are obtained. Biharmonic equation has significant applications in physics and engineering. There is a difficulty to solve the biharmonic equation due to the existence of fourth order derivatives. For this reason, we use the variational iteration method to solve this equation. Test problems, are used to validate this algorithm which is found to be more accurate and efficient than previous ones.     

Generalized Variational Iteration Solution of Soliton for Disturbed KdV Equation

The corresponding solution for a class of disturbed KdV equation is considered using the analytic method. From the generalized variational iteration theory, the problem of solving soliton for the corresponding equation translates into the problem of variational iteration. And then the approximate solution of the soliton for the equation is obtained.     

五阶非线性作用下光纤中类明孤子运动方程的变分研究

当考虑到五阶非线性对光脉冲传输的影响时, 光纤中类明孤子的传输服从含五阶非线性修正项的非线性Schrdinger方程。利用何氏半反推法建立该类明孤子运动方程的变分形式, 然后应用何氏变分法导出该方程基态孤子解的双曲正割表达式。同时, 受何氏指数函数方法的启发, 建立了一种新的高斯表达式。一方面, 基于得到的显式表达式相关学者可进一步研究五阶非线性对光脉冲传输的影响。另一方面, 该求解过程也进一步显示了用何氏变分法求解数学物理中非线性发展方程的简洁有效性。     

中子扩散方程的混合间断有限元法

构造了求解二维两群中子扩散方程的混合间断有限元格式,研制了相应的计算程序.计算结果表明这个格式是可行的.为了提高计算精度,还需进一步深入系统研究     

A Variational Iteration Solving Method for a Class of Generalized Boussinesq Equations

We study a generalized nonlinear Boussinesq equation by introducing a proper functional and constructing the variational iteration sequence with suitable initial approximation. The approximate solution is obtained for the solitary wave of the Boussinesq equation with the variational iteration method.     

求解结构动力响应的卷积型DQ半解析法

通过卷积将原始控制方程构造成包含初始条件的新的具有完整初值问题特征的控制方程.该方程既与Gurtin变分原理一样有合理的数学内涵,又避免了卷积型Gurtin变分原理泛函和计算的繁复.对新的控制方程在时间域取解析函数,在空间域采用离散的DQ法,经对梁的动力响应问题的计算表明,该方法是一种精度好效率高的求解动力响应问题的计算方法.     

一类非线性扰动Burgers方程的孤子变分迭代解法

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.     

三维赤道海气振子模型的近似解

研究了一个赤道Kelvin波的方程. 利用变分迭代解法, 得到了其近似解. 变分迭代方法是一个解析方法, 得到的解还能够继续进行解析运算. 关键词： 变分迭代 近似解 Kelvin     

Variational supersymmetric approach to evaluate Fokker-Planck probability

In this work we introduce a method to determine the time dependent probability density for the one-dimensional Fokker-Planck equation. The treatment is based in an analysis of the Schrödinger equation through the variational method associated to the formalism of supersymmetric quantum mechanics (SQM). The approach uses an ansatz for the superpotential which allows us to obtain the trial functions of the variational method. The hierarchy of effective Hamiltonians permits us to determine the variational eigenfunctions and energies of the excited states to the evaluation of the probability. The symmetric bistable potential is used to illustrate the approach whose results are compared with results obtained by the state-dependent diagonalization method and by direct numerical calculation.     

Residual vibration reduction of a flexible beam deploying from a translating hub

This paper presents a method for reducing the residual vibration of a flexible beam deployed from a translating hub. Whereas previous studies have discussed reducing vibration in translating constant-length beams, this study investigates a vibration reduction method for translating beams of variable length. The partial differential equation of motion for a translating beam is derived and transformed into a variational equation. Based on the discretized equations from the variational equation, the dynamic responses of the flexible beam under translation are analyzed. A vibration reduction method is proposed that is effective for both constant- and variable-length deploying translating beams.     

一个全球气候赤道海气振子模型的变分迭代解法

研究了一个三维赤道海气振子Kelvin波的方程.利用变分迭代解法,得到了对应模型的近似解.变分迭代方法是一个解析方法,得到的解还能够继续进行解析运算. 关键词： 变分迭代 近似解 Kelvin波     

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method’s new role.     

A constrained variational principle for heat conduction

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.     

基于二阶离散变分方法的非线性映射参数估计

提出一种估计非线性映射未知参数的二阶离散变分方法.首先针对非线性离散混沌系统, 利用变分方法导出了伴随方程和目标泛函梯度, 以此为基础利用二阶离散变分方法给出了二阶伴随方程和精确计算Hessian矩阵-向量乘积的显式表达式; 其次设计了估计非线性映射未知参数的新算法, 并以此对Hyperhenón映射和二维抛物映射中的未知参数进行了精确的估计. 数值仿真结果表明了该方法的有效性和优点. 关键词： 非线性映射 参数估计 二阶离散变分方法 伴随方程     

On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method

In this paper, we mainly study the time-space fractional strain wave equation in microstructured solids. He’s variational method, combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation. The main advantage of the variational method is that it can reduce the order of the differential equation, thus simplifying the equation, making the solving process more intuitive and avoiding the tedious solving process.Finally, the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method. The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics.     

极化子新的变分计算

提出了一种新的变分解的方法求解极化子问题，并归结为解一个非线性的微分积分方程。其数值计算的结果正是过去工作所预期的。 关键词：     

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.     

强阻尼广义sine-Gordon方程特征问题的变分迭代法

研究了在数学、力学中广泛出现的一类非线性强阻尼广义sine-Gordon扰动微分方程问题. 首先, 引入行波变换, 求出退化方程的精确解. 再构造一个泛函, 创建了一个变分迭代算法, 最后, 求出原非线性强阻尼广义sine-Gordon扰动微分方程问题的近似行波解析解. 用变分迭代法可得到的各次近似解, 具有便于求解、精度高等特点. 求得的近似解析解弥补了单纯用数值方法的模拟解的不足.