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     

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     

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     

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     

激光脉冲放大器增益通量的广义变分迭代解法

研究一个激光脉冲放大器增益通量的模型. 利用广义变分迭代方法, 首先决定Lagrange乘子,然后构造迭代关系式. 最后得到了相应模型近似解. 关键词： 非线性 变分迭代 激光脉冲放大器     

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     

赤道东太平洋SST的海-气振子模型

研究了一个海-气振子的非线性耦合系统的模型.利用变分迭代原理，首先构造了相应的一组泛函.其次选取其Lagrange乘子.再用广义变分迭代方法得到了海-气振子模型一组解的近似序列. 关键词： 海-气振子 非线性 耦合系统 厄尔尼诺模型     

一类非线性扰动发展方程的广义迭代解

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     

一类广义Canard系统的近似解析解

利用变分迭代理论研究了一类广义Canard系统. 首先引入一组泛函,然后构造了原方程解的迭代关系式,最后得到了问题鸭解的近似解析式. 关键词： 鸭解 解析解 变分迭代     

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.     

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.     

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.     

Modified variational iteration method for an El Ni no Southern Oscillation delayed oscillator

This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Niño Southern Oscillation. The approximate expansions of the delayed differential equation's solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.     

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.     

Numerical simulations of systems of PDEs by variational iteration method

In this Letter, a general framework of the variational iteration method (VIM) is presented for solving systems of linear and nonlinear partial differential equations (PDEs). In VIM, a correction functional is constructed by a general Lagrange's multiplier which can be identified via a variational theory. VIM yields an approximate solution in the form of a rapid convergent series. Comparison with the exact solutions shows that VIM is a powerful method for the solution of linear and nonlinear systems of PDEs.     

Numerical solution of sine-Gordon equation by variational iteration method

In this Letter, variational iteration method (VIM) is applied to obtain approximate analytical solution of the sine-Gordon equation without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.