一类Landau-Ginzburg-Higgs扰动方程孤子的近似解

利用解析方法研究了一类Landau-Ginzburg-Higgs方程. 由广义变分迭代理论得到了相应方程的解,从而得到了对应方程孤子的近似解. 关键词： 孤子 扰动 变分迭代     

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     

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.     

一类扰动洛伦兹系统的解法

研究了一个大气物理中洛伦兹系统的求解问题.首先利用广义变分原理构造一组变分迭代,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.广义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： 洛伦兹方程 变分原理 近似解     

用广义变分迭代理论求一类相对转动动力学方程的解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动扰动动力学方程. 首先利用变分原理构造了广义变分迭代, 其次决定方程的初始近似, 最后通过迭代表示式得到了对应方程的任意次近似解. 关键词： 相对转动 动力系统 变分迭代     

强非线性发展方程孤波近似解

研究了一个强非线性发展方程.利用变分原理，首先构造了相应的泛函.选取Lagrange乘子，再用广义变分迭代方法得到了孤波的任意次精度的近似解. 关键词： 发展方程 非线性 孤立子 近似方法     

Dark and kink soliton solutions of the generalized ZK–BBM equation by iterative scheme

The generalized ZK–BBM equation is solved using iterative scheme of the Adomian decomposition method (ADM) and variational iteration method (VIM). A dark and a kink soliton solutions of the generalized ZK–BBM equation are obtained under initial conditions. The convergence analysis of the ADM and VIM solution shows that these solutions are convergent. The comparison of the ADM and VIM solutions with the exact solution shows that the solutions of the generalized ZK–BBM equation by the iterative methods are almost exact. The absolute errors show that the accuracy and efficiency of the ADM and VIM depend on the problem and its domain. It is found that the iterative scheme of Adomian decomposition method and variational iteration method are quite efficient for the soliton solution of the generalized ZK–BBM equation.     

一个广义扰动mKdV耦合系统2极孤子的近似解

采用了一个简单而有效的技巧,研究了一类扰动mKdV耦合系统.首先利用变分迭代方法求解一个相应的复值函数微分方程2-极孤子的近似解.然后得到了原扰动mKdV耦合系统2-极孤子的近似解.     

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     

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.     

一类量子等离子体类孤波的近似解析解

本文探讨了在一类量子等离子体系统,研究了该系统的非线性动力学扰动方程.利用改进的广义泛函变分迭代方法,求得了对应系统的类孤波近似解析解.     

The sea--air oscillator model of decadal variations in subtropical cells and equatorial Pacific SST

In this paper a time delay equation for sea--air oscillator model is studied. The aim is to create an approximate solving method of nonlinear equation for sea--air oscillator model. Employing the method of variational iteration, it obtains the approximate solution of corresponding equation. This method is an approximate analytic method, which can be often used for analysing other behaviour of the sea surface temperature anomaly of the atmosphere--ocean oscillator model.     

Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation

A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.     

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.     

一类非线性尘埃等离子体孤波解

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     

Variational iteration method for solving an inverse parabolic equation

The variational iteration method is applied to solving an inverse problem of determining an unknown parameter in a linear parabolic equation. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. We get a rapid convergent sequence tending to the exact solution of the inverse problem. To show the efficiency of the present method, some interesting examples are presented.     

海-气耦合动力系统的改进变分迭代解法

研究了一个描述厄尔尼诺和南方涛动振荡物理机理的海-气耦合动力系统.利用改进变分迭代方法 (MVIM)简捷地得到了该非线性模型近似解的展开式.通过与特殊情形下模型精确解的比较,说明获得的MVIM 近似解具有非常好的准确度.     

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.     

Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific

A class of perturbed mechanisms for the western boundary undercurrents in the Pacific is considered. The model of generalized governing equations is studied. Employing the method of variational iteration, an approximate solution of corresponding model is obtained. It is proved from the results that the solution for the variational iteration method can be used for analysing operation of the perturbed mechanism of western boundary undercurrents in the Pacific.     

一类大气浅水波系统的广义变分迭代行波近似解

本文研究了一类非线性浅水波系统,首先构造了相应的泛函. 其次选取Lagrange乘子,再用改进的广义变分迭代方法,得到了相应模型的行波近似解析解. 关键词： 浅水波 非线性 变分迭代 近似解