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首页> 外文期刊>Journal of Mathematical and Computational Science >Exact solution of nonlinear Klein-Gordon equations with quadratic nonlinearity by modified Adomian decomposition method
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Exact solution of nonlinear Klein-Gordon equations with quadratic nonlinearity by modified Adomian decomposition method

机译：改进的Adomian分解法求解具有二次非线性的非线性Klein-Gordon方程的精确解

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In this paper, we used the modified Adomian decomposition method (ADM) to obtain exact solution to Nonlinear Klein-Gordon equation (NK-GE) with quadratic nonlinearity. The paper contains an introduction and the concept of modified ADM for a generalized three-dimensional NK-GE. And, we applied this concept to obtain exact solution to two one-dimensional NK-GE with quadratic nonlinearity. The modified method is based on Taylors series expansion of the source term and implementation on any computer algebra software (Maple, Mathematica, etc) is simple. We discovered that the results of the examples considered are the same as the series solution of those obtained by using any known analytical method. Furthemore, we depicted our findings in three-dimensional surface and contour plots.
机译：在本文中，我们使用改进的Adomian分解方法（ADM）来获得具有二次非线性的非线性Klein-Gordon方程（NK-GE）的精确解。本文介绍了广义三维NK-GE的改进ADM的概念和概念。并且，我们应用此概念来获得具有二次非线性的一维NK-GE的精确解。修改后的方法基于源项的Taylors级数展开，并且在任何计算机代数软件（Maple，Mathematica等）上的实现都很简单。我们发现所考虑的示例的结果与使用任何已知分析方法获得的结果的级数解相同。此外，我们在三维表面和轮廓图中描绘了我们的发现。

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